Menwia, you raise some good ideas, but you're obviously opening many huge cans of worms.
It IS a historical fact, "forget all that politically correct crap" that you can't have Islam without Christianity. But it IS a historical fact, "forget all this politically correct crap", that you can't have America without England, or Rome without Greece/Hellens. Even Spain couldn't really exist the way it does without the Moors. The only way every person could start with the same religion -- in a "historical fact" kind of way -- is if everyone started as the same Civ. And modelling this kind of evolution is pretty damn hard, if not just completely un-Civ-like. (it's too different from Civ 3!) Obviously historical fact can't dictate how things should go in the game.
Assuming that there is an actual benefit to religion beyond that of "well, it's a historical fact"...
Let's assume we can decide which religions are conducive to papal states and crusades. According to you, Islam is. And according to you, Christianity is, but not in the Modern Age. If Christianity forbids said behaviors in the modern age, why? Is it just a fact of evolution that "Crusades are forbidden under this religion in this age", or are their complex factors where some could leverage it and some could not? And if Crusades and Papal States are forbidden, what other benefits do religions offer? With different rules for different religions for different ages the game becomes extremely complicated.
Also, Buddhism is a non-violent religion (it IS a "historical fact") so Crusades would be completely forbidden under it, and exercising a papal state would essentially tie your hands. If Buddhism sucked this much, would anyone ever end up following the path of history and embracing Buddhism? Probably not, if religions were this unbalanced. In other words, when you implement "religious facts" into Civ, the game actually becomes LESS historical because some religions just plain suck. (Pardon the lack of politcally correct crap.) You'd need to change the fundamentals of the game design in order to implement these "historical facts" because you'd need to give people an incentive to play "historically".
And you're right about switching religions. 7 turns of anarchy for a switch from democracy to communism is just barely palattable enough to work. But switching religions has never happened, and there is a reason. It spreads and evolves naturally in different directions, with philosophers popping up and influencing people... and when military domination occurs, it usually brings religion only incidentally, not deliberately. And to have Judaeism influence Islam is about ten times more complicated than having Persia give rise to Iran, not to mention that I think think the two are completely dependant on one another.
So to just say "enh forget the whole natural evolution thing" and just do a "religion switch" is not just a-historical, but loses pretty much any of the gameplay value that comes from religion. Religious wars happen BECAUSE people refuse to change their beliefs. If you can just flip a switch after the crusades and say "you know what, that whole Christianity thing was stupid, we're Muslim now too, so now we can put those crusades behinds us!" -- that pretty much breaks down the gameplay.
Again, to summarize:
You end up trying to simulate the evolution of religion which requires taking it out of the player's hands. Religion has to change, split, re-combine, and spread (usually by force). Religion is a real *force* that works for you and against you, within your nation, and between nations. But this evolution is hard as hell to simulate -- about as impossible as simulating the evolution of the Babylonians to the Americans while leaving room for the Americans to not appear at all.
So you put religious control completely in the hands of the player. And when you do this, the impact of religion the game is gone because it's just a few switches you flip at your convenience instead of a force that you leverage and battle at the same time. The only impact is allowing a player to label a war in the middle ages as "a religious event" instead of a military event -- something that's all in your perception.
Not worth it.