I really love the Orthodox changes in Third Rome, and currently, every Christian denomination now has its own mechanics, as well as a fair degree of flexibility and flavor. Meanwhile, Islam still uses the same mechanic for all three denominations. Yes piety is a powerful mechanic, but it's not all that interesting (even with all the events from Star and Crescent), being the same in Sunni, Shia, and Ibadi, and the mechanic being just a slider to boot. Not to mention the fact that there's no distinction between various the various flavors of Shi'ism.
Unfortunately, I don't know enough about Ibadism to suggest a new mechanic for it, but I have some thoughts on mechanics for Sunnism, Shi'ism (including distinct mechanic suggestions for Twelvers, Ismailis, and Alevis), and a general suggestion for a Caliphate mechanic.
I know my suggestions are probably overly complex, I know my suggestions for Sunnism, Twelverism, and Alevism are probably about as complex as Grand Historian's excellent suggestions for Catholicism, and those haven't been implemented despite the fact that Catholicism is the starting religion for most of the more popular starts and he actually fleshed out the details (whereas I'm proposing only general mechanics, with some details as examples), and so I know that little to none of this is likely to make it into the game. But I'm going to detail my suggestions anyways, because I recently became unemployed and have too much time on my hands. (And yet I am too lazy to make a mod implementing these ideas as proof-of-concept.)
1. Sunnism: Maddhab
Nearly all Sunnis follow one of four schools of jurisprudence, known as maddhab. These aren't really denominations, since a Hanafi will not consider a Hanbali a heretic, but they tend to concentrate in certain areas. I'm thinking that each Sunni province at the start of the game could have a maddhab, which would give small provincial modifiers. At the start of the game, you can pick a madhhab for your nation to adhere to, which gives nation-wide bonuses. If it's the largest madhhab in your country it would be free, otherwise it would cost dip based on the difference between the portion of you Sunni development which follows your maddhab vs the largest madhab, up to 200 dip if your madhab is completely absent. Changing madhhab would cost maybe 150 dip plus the cost of adopting your new madhhab, and reset piety to zero of Sunnism keeps piety.
Newly-converted Sunni provinces would have a base chance of adopting your madhhab equal to 100, with each adjacent Sunni province providing a chance based on its development. So if you're Maliki and you convert a province which borders 30 dev of Shafi'i provinces and 20 dev of Maliki provinces, the province has a 30/150 = 20% chance of being Shafi'i and 120/150 = 80% chance of being Maliki. Provinces may also change school by event, with events that change them to your madhhab (or give you the option of changing it for a cost) being much more common than those which convert it to a different madhhab.
Incidentally, I think this mechanic or a similar one could also work for Vajayrana Buddhism, where various schools play a similar role as the madhhab do in Sunnism.
2. Sunnism: Sufism
During the EU4 timeframe Sufism played a large role in sub-Saharan West Africa and in areas influenced by the Turco-Persian tradition (Anatolia, Persia, Central Asia, and India). I've thought about various ways to represent this, and I think there's two things that would work well to represent Sufism. My first thought was picking a Sufi order to patronize, but A. that's sort of duplicating madhhabs and B. I think the phenomenon of having large numbers of influential Sufi orders in a small area was limited to the Sahel. In Ottoman Turkey the Bektashi had a lot of influence, the Mevlani some, and there were basically no other orders to speak of.
So instead, I think that there's three things that would be useful for Sufism.
2.1: Sufi estate
First, I think that Sunni countries with certain tech groups and/or cultures (representing areas where Sufism was particularly influential during the game's timeframe) should have access to a Sufi estate, which would, among other things, allow the raising of ghazi infantry which take 20% less shock damage, representing how, despite the syncreticism of many Sufi schools, their adherents were among the most fanatical of warriors.
2.2: Sufi shrines
Second, I think that cities which were home to important Sufi shrines should have modifiers a bit like holy sites, though relatively minor ones. Konya (home of the Mevlana order) might plausibly give +.25 yearly legitimacy (even today Rumi is highly revered in Turkey and Persia) or +5% religious unity (Rumi famously allowed non-Muslims to dance with him).
2.3: Disabling Sufism
Thirdly, I think that it should be possible to disable Sufism by decision, giving a bonus to TTF and maybe missionary strength but a malus to tolerance of both heretics and heathens (and maybe relations with heretics). This would represent the various reform movements which tried to root out mysticism and return Islam to its roots. Though Salafism/Wahhabism is the best-known and most successful of these today, you had such movements cropping up at various points throughout history (for example, Zahiriyyah in the Maghreb), mostly in areas inhabited by nomadic Arabs. (Perhaps the decision could require owning or bordering a country with Bedouin culture or in the Maghrebi group, or good relations with a country with that culture, but likely that would be unnecessarily complicated.) Adopting the decision would not destroy the Sufi shrines (destroying Sufi shrines in the name of purity is an innovation after the EU4 era) but would mean you get no longer bonuses from them, and the Sufi estate is disabled if you had access to it. Converting a province with a Sufi shrine to a religion outside the Muslim group would destroy the shrine though.
2.4: Sufism and conversion to Shiism
While Sufi orders generally started out Sunni (Shi'ism tends to be more hierarchal in nature than Sunnism), historically they often adopted elements of Shiism. The Safaviyyah order, for example, switched to Twelverism, conquered Iran, and converted Iran to Shia. And the Bektashi Order played a major role in the development of Alevism in Turkey. So I think that it might be interesting to have event chains which start when a Sunni nation possesses a province with a Sufi shrine either A. a province which is Shia and either bordering or in the same area, or B. a significant part of the nation's development being Shia. Eventually, an event or decision could provide the option to convert to Shia at a cost to stability, with the cost scaling depending on the size of the nation. (There's a reason the Safavids converted while they were still small.)
3. Twelver Shi'ism
3.1: Shia Holy Sites
Yes, I know that this is a clone of Coptic mechanics, however I think it makes even more sense for Shias than it does for Copts. I see no reason an Armenian should care who owns Axum or an Ethiopian should care who owns Yerevan, but Shias (or at least Twelver Shias) are likely to care who owns Karbala and Mashad. My suggestion is that these holy sites should be Mecca, Medina, Jerusalem, Hillah (Karbala and Najaf) and Mashad (Imam Reza Shrine), even knowing that that gives double benefits for controlling Jerusalem and the holy cities. However given that Shi'ism is already quite powerful, maybe the holy sites should only give bonuses to the controller rather than—as with Coptic—for being controlled by anyone of the religion. They could also give set bonuses akin to my suggestion for Sufi shrines (but more powerful bonuses), rather than the flexibility of Coptic if you wanted to further differentiate the mechanic.
3.2: Millenarianism
Twelver Shi'ism believe that the twelfth imam went into occultation, and will return to usher in the end of the world. In this, it is distinguished from most denominations of Islam, and seems unusually prone to Millenarianism. So perhaps for Twelvers it might be interesting to replace piety with a Millenarianism slider. Zero Millenarianism has no benefits or drawbacks, while 100 Millenarianism gives bonuses to technology cost, missionary strength, and morale, but costs tax income, reduces trade power, and increases unrest. Millenarianism would start at zero and could increase (or decrease) through some events, and might also be possible to increase or decrease via dip. (Adjusting it via dip is something I think should be available if holy sites have fixed bonuses, so as to give Shia more agency than "which holy site do I conquer first?")
And yes, I know that this might seem like a step back, since with Third Rome, the last slider which provided both benefits and drawbacks went out the window, and I largely approve of this. However in this proposal you only get the benefits and drawbacks if you choose to increase Millenariusm, and remaining at since remaining at 0 should be fairly easy (at worst maybe costing a small amount of prestige, legitimacy, or dip) in some events, and since I'm suggesting strong bonuses from holy sites, this seems like it might be a fair tradeoff. You can either act like Shi'ism only has the base and holy site bonuses, or you can decide whether the trade off of increasing Millenarianism is worth it. A small, homogeneous Shia state would probably see benefits to having high millenarianism (with only the tax loss being an issue) while it becomes more problematic in a large empire where unrest is an issue and you depend more on trade.
4. Non-Twelver/Ja'fari Shia
There are four Shia denonominations which I strongly think ought to be represented in game in addition to orthodox Twelvers. While today, Twelvers following the Ja'fari school make up the large majority of the world's Shia population, this is mainly because of the Safavid conquest of Iran (as has been noted today, nothing in the Persian culture group south of Tabriz should be Shia at the game start). At the start of the EU4 time frame, Shi'ism whould have been much more heterodox, and I think that Nizari Ismailis, Zaydis, Alawites, and Alevis should all be present in the game. Today, each of these groups is at least as numerous as are Ibadis, and each would be interesting to play.
4.1: Ismailism
The Nizari Ismailis are the second-largest Shia denomination today, and at the start of the EU4 period might well have been the largest. The Fatamid Caliphate was Ismaili, and after its decline the Nizari tradition became the dominant version of Ismailism. Though most Nizaris follow the orthodox Ja'fari school of jurisprudence (same as Iranian Twelvers), Nizarism emphasizes a continuing, hereditary imamate. This could be represented by something a bit like the Catholic Curia but without a Papal controller, essentially accruing imam authority you use to buy short-term benefits.
The biggest problem with Ismailism is that it's widely spread; even today it's a majority really only in the Pamirs and parts of Kashmir. I think the most obvious solution would be to make Shia Baltistan (the province) and Kashmir (the country) Ismaili, and possibly Yedishkul as well. Now the Shah Miri Dynasty was actually Sunni, but is Shia in game, so if you're doing that, it doesn't matter what variety of Shiism they weren't. Alternatively, make Kashmir Sunni, but give it an event chain that gives the option of embracing Ismailism.
4.2: Zaidiyyah
The Zaydis inhabit the provinces in Yemen represented by having Shia provinces, and would have been the majority in Najran and probably the majority in Asir and Jazan, all in neighboring Hejaz. In games I've played close enough to observe Yemen but not close enough to conquer it out the gate, Yemen attempts to convert those provinces almost immediately. A little over half the time it succeeds, and the rest of the time it spawns Shia rebels which convert it to Shia, which is actually kind of realistic historically, since at the start of the game Yemen was experiencing internal turmoil and a dynasty change, Zaydi imams throughout the game period were an alternative center of power, and they eventually managed to establish a Zaydi state.
Zaydis follow their own school of jurisprudence as well as their own succession for the imamate, and the imams they have in the EU4 period are distinct from the imams who descended from Ali, of whom they only recognize five (hence the alternative name "Fivers"). Given the attempts of the Zaydi imams to establish temporal control over greater Yemen, perhaps they could, instead of piety, use mechanics similar to Orthodox mechanics in third Rome: You have imamate authority, and more is always good, but you can spend it on additional bonuses (not icons though, obviously not icons).
4.3: Shi'ism and relations
I feel like if Zaydis and Ismailis were added they should have halved or even no relationship penalties with other Shias. Today, Twelvers accept both groups as Shia, though I'm not sure whether that would have been true in the EU4 time period. By contrast Alawites and Alevis, despite being notionally Twelvers, have often been considered ghulat by other Shia (both denominations venerate Ali, hence the names, and have been accused of elevating him to the status of divinity), and have often accused of being heathens/apostates by Sunnis. So they should probably get zero or reduced relations penalties with each other, normal relations penalties with other Shia, and doubled relations penalties with Sunnis.
4.4: Alawites
The Alawites today constitute the relative majority in the in-game provinces of Antioch and Tarabulus al-Sham, though I don't know whether that was the case at the time. (Also, I think Tarabalus-al-Sham should be divided into 2-4 provinces: Sunni Tarabalus, Alawite Latakia, Alawite Tartus, and Twelver Baalbek.) Unfortunately, while Alawite theology is really interesting, including beliefs in a trinity and reincarnation, and seems like it has the potential for a lot of really interesting flavor events, I don't have an idea for an obvious mechanic for Alawiyyah mostly because I know literally nothing about how it's actually practiced.
4.5: Alevism
The Alevis probably wouldn't have been the majority in any in-game provinces (in modern Turkey they are a majority only in Tunceli), but they are today a significant minority in the in-game provinces of Amasya, Sivas, and Erzincan, though all of these provinces are Turkish culture and Alevism is also practiced by a lot of Kurds. Hopefully the provinces of Turkey will be re-worked in a future patch, allowing a patchwork of Alevi and Sunni provinces. I also think that converting to Alevism under certain conditions should be possible (see point three), though with a stability penalty which increases with development. It's not hard to imaging Aq Qoyunlu or Karaman embracing Alevism; it's much harder to imagine the Ottomans doing so (particularly since being a member of the strictly monagamous Alevi should absolutely disable any government which depends on harams).
I think Alevis should be able to use the Sufi mechanics I proposed earlier for Sunnism, and I also have an additional, Alevi-specific mechanic suggestion. I'm not super-confident about it (my knowledge of Alevism is based on talking to a few not-very-observent Alevis in Istanbul and Izmir plus Wikipedia), but I'll put it out there regardless.
The Alevi mechanic I think would be interesting relates to the twelve services performed at Alevi Cems. I think that Alevi rulers should be able to pick a service to perform at the cem (or possibly to reject performing a service at a small ticking prestige penalty). Unlike cults or personal deities, these would not be consistent throughout a leader's life. Either events would allow the leader to change the role the leader plays, or the ruler would be able to change their role manually after a cooldown. Since these bonuses would be more flexible than the bonuses from most other religions, and since Alevis would get permanent bonuses from Sufi shrines, I think they should be relatively weak, but still add flavor. Being Gözcü, for example, might represent a -.5 to national unrest; being Süpürgeci might give a -2.5% to build costs, being Sakaci might represent a -2.5% to development costs and development costs.
The roles of Murshid and Rehber should be limited to rulers who are also Dedes, and becoming a Dede should only be possible through event (with ruler traits and diplomatic and administrative skill making it more likely), but should be correspondingly more powerful. Being Murshid might give +1 yearly legitimacy, being Rehber might represent give +20% institution spread. Being Murshid should not be a role that can be given up, but if the Alevis had events related to the four doors, a ruler over 60 might be able to give up the role by passing on to Marifa.
The Alevi concept of Müsahiplik or spiritual brotherhood also presents some interesting possibilities. I'm not sure how tricky this would be to code, but imagine male Alevi rulers being able to have a spiritual brother in addition to an heir and a consort. If the ruler dies before his heir is of age, the player would have a choice between a Müsahiplik regency and a consort regency, and might also have the option of making his spiritual brother his heir, at the cost of legitimacy.
Again, my knowledge of Alevism is rather limited. I don't know whether the roles (other than Murshid and Rehber) can be taken by anyone, I don't know whether people switch roles, and I don't know whether a secular ruler could even be a Dede. I don't know whether a spiritual brother might also serve as a sort of godparent, or whether it would be plausible to appoint one as heir. There seem to be a lot of Turks on these forums so I'm hoping at least one of them might be an observant Alevi who can comment on my ideas here.
4.6: Sidebar on the Druze
The Druze I'm going to mention only because I expect someone to bring them up if I don't. The Druze are a heterodox offshoot of Ismailism, and quite interesting. It would be possible to carve Jabal-al-Druze out of Aljoun to have a Druze-majority province. On the other hand, the Druze don't accept converts. I've been trying to write a proposal similar to this one for expanding the Zoroastrian group, and have been similarly stumped by the Yezidis and Mandeans, who like the Druze don't accept converts (and also like the Druze don't have an EU4 province they're a majority in). I'd love to see the Druze in game, but at the moment I haven't the slightest idea how to handle them. If I come up with something I'll include it in my Zoroastrian reform proposal (even though they belong in the Muslim religious group), but for now I've got absolutely nothing.
5. The Caliphate
Right now, the Caliphate isn't really well-represented in-game. Any Sunni ruler with military skill of at least three can call themself Caliph. However the Ottoman Empire re-establishing the Caliphate was actually a major event. I think that any Muslim ruler (or possibly any Sunni, Ibadi, Twelver, Ismaili, or Zaydi ruler, since I'm not sure how plausible an Alevi/Alawite Caliphate would be, though the Fatimid Caliphate shows it should be more than Sunni) who controls Mecca and Medina (either directly or through a vassal and is a great power (if RoM is enabled) or empire rank (if playing without RoM), should be able to re-establish the Caliphate.
Once re-established, the Caliphate would have an interface in the bottom right corner, with the Caliph being something a bit like Papal Controller and a bit like Emperor of China (representing the Caliph's temporal and religious authority), but less powerful than either. The Caliph should get some permanent bonuses like papal controller (in fact an extra diplomat and extra advisor both seem reasonable), and have something akin to mandate which can be spent on bonuses similar to decrees. I'm thinking that caliphal authority could be accrued passively for being DoTF and actively for honoring DoTF CTAs and using the DoTF CB. It could also be gained by having countries acknowledge your authority. Though countries who acknowledge your authority wouldn't be subjects even in the loose sense of tributaries, they would increase passive accrual of caliphal authority and might allow additional diplomatic actions.
The only such action I have a suggestion for now is "appoint amir." If a Muslim state acknowledges your authority and borders a Muslim state which doesn't do so, you can appoint the loyal Muslim state amir of an adjacent area owned by the disloyal Muslim state, which would give the loyal Muslim ruler claims on that entire area (and possibly a CB which reduces AE for taking them). Appointing amirs would cost caliph authority (either a flat amount or based on development), but if your loyal amir conquers that area within a set time, you can Caliph authority.
6. Marionites
Yes, the Marionites are Christian, not Muslim, and being doctrinally Catholic don't merit their own religion. However given that they're in the Middle East and I can't see myself doing a whole post like this for the Christian religious group (though I would like to do so for Dharmic and Zoroastrian), I thought I'd mention my thoughts on them here.
It annoys me how quickly Lebanon gets rapidly converted every game, considering that Lebanon was majority Marionite right up until the middle of the twentieth century, and they strongly resisted attempts at conversion. (The one time I saw Lebanon get released, it was Sunni.) It would help if Sidon got a "Marionites" modiifier with -5% missionary strength (similar to religious center modifiers) which remains as long as the province remains Catholic? Also it would be nice if Sidon were divided into Beirut (Marionite Catholic) and Tyre (Twelver Shia).
Unfortunately, I don't know enough about Ibadism to suggest a new mechanic for it, but I have some thoughts on mechanics for Sunnism, Shi'ism (including distinct mechanic suggestions for Twelvers, Ismailis, and Alevis), and a general suggestion for a Caliphate mechanic.
I know my suggestions are probably overly complex, I know my suggestions for Sunnism, Twelverism, and Alevism are probably about as complex as Grand Historian's excellent suggestions for Catholicism, and those haven't been implemented despite the fact that Catholicism is the starting religion for most of the more popular starts and he actually fleshed out the details (whereas I'm proposing only general mechanics, with some details as examples), and so I know that little to none of this is likely to make it into the game. But I'm going to detail my suggestions anyways, because I recently became unemployed and have too much time on my hands. (And yet I am too lazy to make a mod implementing these ideas as proof-of-concept.)
1. Sunnism: Maddhab
Nearly all Sunnis follow one of four schools of jurisprudence, known as maddhab. These aren't really denominations, since a Hanafi will not consider a Hanbali a heretic, but they tend to concentrate in certain areas. I'm thinking that each Sunni province at the start of the game could have a maddhab, which would give small provincial modifiers. At the start of the game, you can pick a madhhab for your nation to adhere to, which gives nation-wide bonuses. If it's the largest madhhab in your country it would be free, otherwise it would cost dip based on the difference between the portion of you Sunni development which follows your maddhab vs the largest madhab, up to 200 dip if your madhab is completely absent. Changing madhhab would cost maybe 150 dip plus the cost of adopting your new madhhab, and reset piety to zero of Sunnism keeps piety.
Newly-converted Sunni provinces would have a base chance of adopting your madhhab equal to 100, with each adjacent Sunni province providing a chance based on its development. So if you're Maliki and you convert a province which borders 30 dev of Shafi'i provinces and 20 dev of Maliki provinces, the province has a 30/150 = 20% chance of being Shafi'i and 120/150 = 80% chance of being Maliki. Provinces may also change school by event, with events that change them to your madhhab (or give you the option of changing it for a cost) being much more common than those which convert it to a different madhhab.
Incidentally, I think this mechanic or a similar one could also work for Vajayrana Buddhism, where various schools play a similar role as the madhhab do in Sunnism.
2. Sunnism: Sufism
During the EU4 timeframe Sufism played a large role in sub-Saharan West Africa and in areas influenced by the Turco-Persian tradition (Anatolia, Persia, Central Asia, and India). I've thought about various ways to represent this, and I think there's two things that would work well to represent Sufism. My first thought was picking a Sufi order to patronize, but A. that's sort of duplicating madhhabs and B. I think the phenomenon of having large numbers of influential Sufi orders in a small area was limited to the Sahel. In Ottoman Turkey the Bektashi had a lot of influence, the Mevlani some, and there were basically no other orders to speak of.
So instead, I think that there's three things that would be useful for Sufism.
2.1: Sufi estate
First, I think that Sunni countries with certain tech groups and/or cultures (representing areas where Sufism was particularly influential during the game's timeframe) should have access to a Sufi estate, which would, among other things, allow the raising of ghazi infantry which take 20% less shock damage, representing how, despite the syncreticism of many Sufi schools, their adherents were among the most fanatical of warriors.
2.2: Sufi shrines
Second, I think that cities which were home to important Sufi shrines should have modifiers a bit like holy sites, though relatively minor ones. Konya (home of the Mevlana order) might plausibly give +.25 yearly legitimacy (even today Rumi is highly revered in Turkey and Persia) or +5% religious unity (Rumi famously allowed non-Muslims to dance with him).
2.3: Disabling Sufism
Thirdly, I think that it should be possible to disable Sufism by decision, giving a bonus to TTF and maybe missionary strength but a malus to tolerance of both heretics and heathens (and maybe relations with heretics). This would represent the various reform movements which tried to root out mysticism and return Islam to its roots. Though Salafism/Wahhabism is the best-known and most successful of these today, you had such movements cropping up at various points throughout history (for example, Zahiriyyah in the Maghreb), mostly in areas inhabited by nomadic Arabs. (Perhaps the decision could require owning or bordering a country with Bedouin culture or in the Maghrebi group, or good relations with a country with that culture, but likely that would be unnecessarily complicated.) Adopting the decision would not destroy the Sufi shrines (destroying Sufi shrines in the name of purity is an innovation after the EU4 era) but would mean you get no longer bonuses from them, and the Sufi estate is disabled if you had access to it. Converting a province with a Sufi shrine to a religion outside the Muslim group would destroy the shrine though.
2.4: Sufism and conversion to Shiism
While Sufi orders generally started out Sunni (Shi'ism tends to be more hierarchal in nature than Sunnism), historically they often adopted elements of Shiism. The Safaviyyah order, for example, switched to Twelverism, conquered Iran, and converted Iran to Shia. And the Bektashi Order played a major role in the development of Alevism in Turkey. So I think that it might be interesting to have event chains which start when a Sunni nation possesses a province with a Sufi shrine either A. a province which is Shia and either bordering or in the same area, or B. a significant part of the nation's development being Shia. Eventually, an event or decision could provide the option to convert to Shia at a cost to stability, with the cost scaling depending on the size of the nation. (There's a reason the Safavids converted while they were still small.)
3. Twelver Shi'ism
3.1: Shia Holy Sites
Yes, I know that this is a clone of Coptic mechanics, however I think it makes even more sense for Shias than it does for Copts. I see no reason an Armenian should care who owns Axum or an Ethiopian should care who owns Yerevan, but Shias (or at least Twelver Shias) are likely to care who owns Karbala and Mashad. My suggestion is that these holy sites should be Mecca, Medina, Jerusalem, Hillah (Karbala and Najaf) and Mashad (Imam Reza Shrine), even knowing that that gives double benefits for controlling Jerusalem and the holy cities. However given that Shi'ism is already quite powerful, maybe the holy sites should only give bonuses to the controller rather than—as with Coptic—for being controlled by anyone of the religion. They could also give set bonuses akin to my suggestion for Sufi shrines (but more powerful bonuses), rather than the flexibility of Coptic if you wanted to further differentiate the mechanic.
3.2: Millenarianism
Twelver Shi'ism believe that the twelfth imam went into occultation, and will return to usher in the end of the world. In this, it is distinguished from most denominations of Islam, and seems unusually prone to Millenarianism. So perhaps for Twelvers it might be interesting to replace piety with a Millenarianism slider. Zero Millenarianism has no benefits or drawbacks, while 100 Millenarianism gives bonuses to technology cost, missionary strength, and morale, but costs tax income, reduces trade power, and increases unrest. Millenarianism would start at zero and could increase (or decrease) through some events, and might also be possible to increase or decrease via dip. (Adjusting it via dip is something I think should be available if holy sites have fixed bonuses, so as to give Shia more agency than "which holy site do I conquer first?")
And yes, I know that this might seem like a step back, since with Third Rome, the last slider which provided both benefits and drawbacks went out the window, and I largely approve of this. However in this proposal you only get the benefits and drawbacks if you choose to increase Millenariusm, and remaining at since remaining at 0 should be fairly easy (at worst maybe costing a small amount of prestige, legitimacy, or dip) in some events, and since I'm suggesting strong bonuses from holy sites, this seems like it might be a fair tradeoff. You can either act like Shi'ism only has the base and holy site bonuses, or you can decide whether the trade off of increasing Millenarianism is worth it. A small, homogeneous Shia state would probably see benefits to having high millenarianism (with only the tax loss being an issue) while it becomes more problematic in a large empire where unrest is an issue and you depend more on trade.
4. Non-Twelver/Ja'fari Shia
There are four Shia denonominations which I strongly think ought to be represented in game in addition to orthodox Twelvers. While today, Twelvers following the Ja'fari school make up the large majority of the world's Shia population, this is mainly because of the Safavid conquest of Iran (as has been noted today, nothing in the Persian culture group south of Tabriz should be Shia at the game start). At the start of the EU4 time frame, Shi'ism whould have been much more heterodox, and I think that Nizari Ismailis, Zaydis, Alawites, and Alevis should all be present in the game. Today, each of these groups is at least as numerous as are Ibadis, and each would be interesting to play.
4.1: Ismailism
The Nizari Ismailis are the second-largest Shia denomination today, and at the start of the EU4 period might well have been the largest. The Fatamid Caliphate was Ismaili, and after its decline the Nizari tradition became the dominant version of Ismailism. Though most Nizaris follow the orthodox Ja'fari school of jurisprudence (same as Iranian Twelvers), Nizarism emphasizes a continuing, hereditary imamate. This could be represented by something a bit like the Catholic Curia but without a Papal controller, essentially accruing imam authority you use to buy short-term benefits.
The biggest problem with Ismailism is that it's widely spread; even today it's a majority really only in the Pamirs and parts of Kashmir. I think the most obvious solution would be to make Shia Baltistan (the province) and Kashmir (the country) Ismaili, and possibly Yedishkul as well. Now the Shah Miri Dynasty was actually Sunni, but is Shia in game, so if you're doing that, it doesn't matter what variety of Shiism they weren't. Alternatively, make Kashmir Sunni, but give it an event chain that gives the option of embracing Ismailism.
4.2: Zaidiyyah
The Zaydis inhabit the provinces in Yemen represented by having Shia provinces, and would have been the majority in Najran and probably the majority in Asir and Jazan, all in neighboring Hejaz. In games I've played close enough to observe Yemen but not close enough to conquer it out the gate, Yemen attempts to convert those provinces almost immediately. A little over half the time it succeeds, and the rest of the time it spawns Shia rebels which convert it to Shia, which is actually kind of realistic historically, since at the start of the game Yemen was experiencing internal turmoil and a dynasty change, Zaydi imams throughout the game period were an alternative center of power, and they eventually managed to establish a Zaydi state.
Zaydis follow their own school of jurisprudence as well as their own succession for the imamate, and the imams they have in the EU4 period are distinct from the imams who descended from Ali, of whom they only recognize five (hence the alternative name "Fivers"). Given the attempts of the Zaydi imams to establish temporal control over greater Yemen, perhaps they could, instead of piety, use mechanics similar to Orthodox mechanics in third Rome: You have imamate authority, and more is always good, but you can spend it on additional bonuses (not icons though, obviously not icons).
4.3: Shi'ism and relations
I feel like if Zaydis and Ismailis were added they should have halved or even no relationship penalties with other Shias. Today, Twelvers accept both groups as Shia, though I'm not sure whether that would have been true in the EU4 time period. By contrast Alawites and Alevis, despite being notionally Twelvers, have often been considered ghulat by other Shia (both denominations venerate Ali, hence the names, and have been accused of elevating him to the status of divinity), and have often accused of being heathens/apostates by Sunnis. So they should probably get zero or reduced relations penalties with each other, normal relations penalties with other Shia, and doubled relations penalties with Sunnis.
4.4: Alawites
The Alawites today constitute the relative majority in the in-game provinces of Antioch and Tarabulus al-Sham, though I don't know whether that was the case at the time. (Also, I think Tarabalus-al-Sham should be divided into 2-4 provinces: Sunni Tarabalus, Alawite Latakia, Alawite Tartus, and Twelver Baalbek.) Unfortunately, while Alawite theology is really interesting, including beliefs in a trinity and reincarnation, and seems like it has the potential for a lot of really interesting flavor events, I don't have an idea for an obvious mechanic for Alawiyyah mostly because I know literally nothing about how it's actually practiced.
4.5: Alevism
The Alevis probably wouldn't have been the majority in any in-game provinces (in modern Turkey they are a majority only in Tunceli), but they are today a significant minority in the in-game provinces of Amasya, Sivas, and Erzincan, though all of these provinces are Turkish culture and Alevism is also practiced by a lot of Kurds. Hopefully the provinces of Turkey will be re-worked in a future patch, allowing a patchwork of Alevi and Sunni provinces. I also think that converting to Alevism under certain conditions should be possible (see point three), though with a stability penalty which increases with development. It's not hard to imaging Aq Qoyunlu or Karaman embracing Alevism; it's much harder to imagine the Ottomans doing so (particularly since being a member of the strictly monagamous Alevi should absolutely disable any government which depends on harams).
I think Alevis should be able to use the Sufi mechanics I proposed earlier for Sunnism, and I also have an additional, Alevi-specific mechanic suggestion. I'm not super-confident about it (my knowledge of Alevism is based on talking to a few not-very-observent Alevis in Istanbul and Izmir plus Wikipedia), but I'll put it out there regardless.
The Alevi mechanic I think would be interesting relates to the twelve services performed at Alevi Cems. I think that Alevi rulers should be able to pick a service to perform at the cem (or possibly to reject performing a service at a small ticking prestige penalty). Unlike cults or personal deities, these would not be consistent throughout a leader's life. Either events would allow the leader to change the role the leader plays, or the ruler would be able to change their role manually after a cooldown. Since these bonuses would be more flexible than the bonuses from most other religions, and since Alevis would get permanent bonuses from Sufi shrines, I think they should be relatively weak, but still add flavor. Being Gözcü, for example, might represent a -.5 to national unrest; being Süpürgeci might give a -2.5% to build costs, being Sakaci might represent a -2.5% to development costs and development costs.
The roles of Murshid and Rehber should be limited to rulers who are also Dedes, and becoming a Dede should only be possible through event (with ruler traits and diplomatic and administrative skill making it more likely), but should be correspondingly more powerful. Being Murshid might give +1 yearly legitimacy, being Rehber might represent give +20% institution spread. Being Murshid should not be a role that can be given up, but if the Alevis had events related to the four doors, a ruler over 60 might be able to give up the role by passing on to Marifa.
The Alevi concept of Müsahiplik or spiritual brotherhood also presents some interesting possibilities. I'm not sure how tricky this would be to code, but imagine male Alevi rulers being able to have a spiritual brother in addition to an heir and a consort. If the ruler dies before his heir is of age, the player would have a choice between a Müsahiplik regency and a consort regency, and might also have the option of making his spiritual brother his heir, at the cost of legitimacy.
Again, my knowledge of Alevism is rather limited. I don't know whether the roles (other than Murshid and Rehber) can be taken by anyone, I don't know whether people switch roles, and I don't know whether a secular ruler could even be a Dede. I don't know whether a spiritual brother might also serve as a sort of godparent, or whether it would be plausible to appoint one as heir. There seem to be a lot of Turks on these forums so I'm hoping at least one of them might be an observant Alevi who can comment on my ideas here.
4.6: Sidebar on the Druze
The Druze I'm going to mention only because I expect someone to bring them up if I don't. The Druze are a heterodox offshoot of Ismailism, and quite interesting. It would be possible to carve Jabal-al-Druze out of Aljoun to have a Druze-majority province. On the other hand, the Druze don't accept converts. I've been trying to write a proposal similar to this one for expanding the Zoroastrian group, and have been similarly stumped by the Yezidis and Mandeans, who like the Druze don't accept converts (and also like the Druze don't have an EU4 province they're a majority in). I'd love to see the Druze in game, but at the moment I haven't the slightest idea how to handle them. If I come up with something I'll include it in my Zoroastrian reform proposal (even though they belong in the Muslim religious group), but for now I've got absolutely nothing.
5. The Caliphate
Right now, the Caliphate isn't really well-represented in-game. Any Sunni ruler with military skill of at least three can call themself Caliph. However the Ottoman Empire re-establishing the Caliphate was actually a major event. I think that any Muslim ruler (or possibly any Sunni, Ibadi, Twelver, Ismaili, or Zaydi ruler, since I'm not sure how plausible an Alevi/Alawite Caliphate would be, though the Fatimid Caliphate shows it should be more than Sunni) who controls Mecca and Medina (either directly or through a vassal and is a great power (if RoM is enabled) or empire rank (if playing without RoM), should be able to re-establish the Caliphate.
Once re-established, the Caliphate would have an interface in the bottom right corner, with the Caliph being something a bit like Papal Controller and a bit like Emperor of China (representing the Caliph's temporal and religious authority), but less powerful than either. The Caliph should get some permanent bonuses like papal controller (in fact an extra diplomat and extra advisor both seem reasonable), and have something akin to mandate which can be spent on bonuses similar to decrees. I'm thinking that caliphal authority could be accrued passively for being DoTF and actively for honoring DoTF CTAs and using the DoTF CB. It could also be gained by having countries acknowledge your authority. Though countries who acknowledge your authority wouldn't be subjects even in the loose sense of tributaries, they would increase passive accrual of caliphal authority and might allow additional diplomatic actions.
The only such action I have a suggestion for now is "appoint amir." If a Muslim state acknowledges your authority and borders a Muslim state which doesn't do so, you can appoint the loyal Muslim state amir of an adjacent area owned by the disloyal Muslim state, which would give the loyal Muslim ruler claims on that entire area (and possibly a CB which reduces AE for taking them). Appointing amirs would cost caliph authority (either a flat amount or based on development), but if your loyal amir conquers that area within a set time, you can Caliph authority.
6. Marionites
Yes, the Marionites are Christian, not Muslim, and being doctrinally Catholic don't merit their own religion. However given that they're in the Middle East and I can't see myself doing a whole post like this for the Christian religious group (though I would like to do so for Dharmic and Zoroastrian), I thought I'd mention my thoughts on them here.
It annoys me how quickly Lebanon gets rapidly converted every game, considering that Lebanon was majority Marionite right up until the middle of the twentieth century, and they strongly resisted attempts at conversion. (The one time I saw Lebanon get released, it was Sunni.) It would help if Sidon got a "Marionites" modiifier with -5% missionary strength (similar to religious center modifiers) which remains as long as the province remains Catholic? Also it would be nice if Sidon were divided into Beirut (Marionite Catholic) and Tyre (Twelver Shia).
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Changing "Maddhab" should cost admin points, though.
