@Jomini - que?! Zaporizhzhia Sich was not a polish-russian condominium!
As per the treaty of Andrusovo it was. Which is about 15 years after formal organization (splitting of the Host into the Hetmanate and Sich). The game database begins with the Hetmanate in 1555 which, in western history, denotes a different polity from which the Sich was derived in 1654. In all cases, these polities were not synonomous withe Zaporizhian Host which crossed borders and did not follow subject-overlord modeling.
When Turkish Sultan written protests on the Zaporozhian Cossacks attacks on merchant ships on the Black Sea, he wrote them to the Polish-Lithuanian king. Not to the Tsar of Russia. Khmelnitsky said that the Commonwealth is as mother, and the king (king of PLC) is as father. Zaporozhian Cossacks used its influence in Moscow, because they were losing the uprising. NOT because Russia was a co-colonizer. Sich has acted in the period 1556-1775, not "two decades".
List of major Zaporizhzhian Cossack uprisings:
Kosiński Uprising (1591-1593) - antifeudal
Nalyvaiko Uprising (1594-1596) - private conflict and religious
Zhmaylo Uprising (1625) - conflict of interest of the king and Sich (the king wanted peace with the Crimean Khanate; the Cossacks war) and religious
Fedorovych Uprising (1630) - antifeudal, religious, conflict of interest of the king and Sich (Cossack piracy and raids on muslims lands)
Sulyma Uprising (1635) - antifeudal
Pavlyuk Uprising (1637) - nationalist and antifeudal
Ostryanyn Uprising (1638) - antifeudal
Khmelnytsky Uprising (1648-1655) - private conflict, antifeudal, nationalist, conflict of interest of the Senat, Sejm and Sich (Sejm and the Senate wanted peace with Turkey, Sich wanted war) and religious
Paliy Uprising (1702-1704) - against the liquidation of their class
All... vs PLC.
Russia eliminated the Sich because it was the center of anarchism.
I believe this is a question of terminology, I recognize many of these uprisings, but most are the effect of the Zaporizhian Host under the history terms I learned at MCWAR. As noted above, as a polity the "Sich" doesn't refer to anything until Pereyaslav. I realize that my local language skills are non-existent so my apologies if this schema is not what is used locally.
When it comes to game terms, a lot of these should show up in the rebel mechanisms, not the vassal ones. For instance the Sulyma Uprising involved Cossacks in Cherkasy, which the game currently awards to the PLC proper in the game database. The Nalyvaiko Uprising was in Bratislav, which again is PLC proper territory.
Regardless, the Cossack polities proved to be disloyal to
everyone, not just Catholic Poles. It wasn't like once the Orthodox Russians took over, everyone got along well. If anything, there was greater antagonism between the co-religionists.
But let's look at some other polities. Like say the subjects of the OE. Who was more loyal the Transylvanians or Berbers? How about the British - the Protestant Thirteen Colonies of the Catholic Canadian ones? Or how about, say every Catholic vassal in Italy that ever rebelled. Or perhaps, every single Protestant or Reformed puppet state under Napoleon's Catholic France that failed to rebel even when they had greater combined military power than France proper.
In the grand sweep of EUIV history, at best vassal religion has minimal impact on how often the vassal betrayed the overlord or how often it rebelled towards independence. Now sure, if the overlord tries to impose religious changes on the subject (e.g. Reformed Scotland being commanded by Protestant England to adopt episcopacy and the prayer book - i.e. Protestantism proper), then sure let the Liberty Desire ring. But the whole point of granting a vassal autonomy and letting them control their own religious matters was to remove religion from the grievance list and better allow the central state to maintain some control of the territory without suffering unwarranted costs.