True, but there is a big difference between say a Shia holding Mecca and how it would impact a Sunni, vs. a Christian holding Mecca.
The First Crusade was called by the Pope, and answered by (Catholic) Lords and Kings to defend Christians, ie the Orthodox Byzantines. In reality I would not truly define these as entirely separate religions, but more as competing theological doctrines (Definitely in the Shia vs. Sunni case, but also in the various versions of Christianity).
Certainly some merit in the original suggestion, but it's all an issue of balance.
Whether you define them as different religions or "competing doctrines", there's still the fact that they are in conflict. A gain for Sunni muslims is not and should not translate into moral authority for Shia or Ibadi.
As for Christianity, yes, the first crusade was both Catholics and Orthodox working together to wage war on Islam, but the fact that a crusade was called for political reasons is pretty irrelevant as to whether or not the sites held by the Catholic world helps out the moral authority of Orthodoxy. I mean, the entire Great Schism is a pretty obvious reason to think that they shouldn't contribute positively to the moral authority of each other.
Remember, controlling holy sites translates in-game into a positive bonus for MA, not a penalty for not holding one. And therefore, you should be thinking of it in terms of "holding a holy site helps improve the legitimacy of a faith" instead of "having a holy site controlled by another religion actively hurts the faith." But that means you actually need to control it to get a bonus for it, and this makes sense.
If you want to argue for the current mechanics to be changed in order to reflect what you were talking about, sure. But that still shouldn't be modeled by giving everyone of the same religious group a bonus to MA for having a holy site controlled by someone of the same religion. Rather, the correct way to model that is to introduce an actual penalty to MA if a holy site is controlled by a different religious group or heresy.
And I'd actually kind of like to see that, seeing as how it's still possible (and incredibly easy) for, say, Catholocism to have 100% MA even if no holy sites are controlled and the Catholic world is reduced to some backwater duchy somewhere.