I agree with what Djarum Kretek suggests...
Yes it's true part of the fun of the game is that u can change history in the game... but the word "change" itself implies that there was a accepted original blueprint. Without it there wouldn't be "change"...
What makes this game so fun for people, including those that believe in "changing history", is that the game starts out LIKE THE REAL WORLD as MUCH as possible, THEN the player can "change" history... it's the sense of power from being able to "change" the world
If we have, for example, Confucian/Taoist missionaries, then we're not changing history, history is changed for us. In other words, we might as well be playing games that have civs like Elfs, Humans, Uruks... or whteva...
isn't there any other way we may play with religion? Here are some that I thought of...
1. After the first civ successfully researched Religion, no other civ may (which is true in real life same religions don't spring up in differnet places)... and the only way these civs can get the religion is by getting it from the civ that invented it.
2. Build religion related improvements in cities close to borders... so the cities of the other civs can get affected by it.
2.1 Wonders/small wonders of religion's location. if the wonders are built close to other civs, that should increase the religion's influence.
3. Cities that do trade are slowly exposed to religion, then just like flipping allegience in Civ3, the weaker cultured city would convert. (Distance can play a role in this) Cities of the same civ can also be religiously strengthened by trading with more cities under the same religion.
3.1 Seafaring trade to an inferior city would automatically bring religion over, and the speed of convertion will be quicker.
4. Wonders/small wonders would serve as catalysts, and create Age of Religion. Each religion should have 1 great wonder and maybe 2 small wonders, so other nations that was gifted the religion by the origianl inventor might be able to build influence of its own, and big empires can have more wonders on different borders
4.1 Small wonders would expire in industrial/moderm epoches, while great wonders stay effective.
5. In modern times religion becomes city-specific. While Civ can maintain state religion and cities that believe in that religion gets happiness/health bonus, other cities can b of other religions. (which would serve to remind the player that they might b in danger of losing that city)
6. Religious Leaders. For example, once a Daoist civ gets Lao Zi, u can have him rush a religious wonder, set up a religious mecca (which can b somewhere far from capital for various bonus to neighboring cities like the Forbidden Palace does for corruption), or send to friendly nation's capital and instanting convert the other civ.