CiV has to have a different system for religion. I had the suggestion of adding a religious policy tree. We could call them RPs. Each tree is a different religion, in Ancient and Classical times, the first three early religion trees would be open. What could these early possibilities be. Let's say Tribal or Pagan, Two sets of Polythesistic religions, one based on Mesopotamian beliefs, that there is no afterlife. The person is basically a vessel put on earth to do the bidding of the gods. The second form of religion instills the belief in the people who practice it, that there is an afterlife gained upon death. Indicitive of the Old Kingdom of Egypt, that afterlife can be shared by all, not just Pharaoh. Every person has a ba, which remains attached to the body after death, the ka, or life force, through funeral rituals is released, and rejoined to the ba, into an akh a form of afterlife. It was belief that the corpse be preserved so the ka could find the ba each night to recieve new life.
This form of Polytheism based on belief in an afterlife, could promote happiness, people live knowing as long as they live a good life, they will be rewarded with a glorious afterlife, they are not just some vessel for their gods amusement, or pleasure. The feeling is instilled that they are actually worth something.
Asian religions would have to be added as well. I think a religious policy tree would make the game more interesting. It could help give civs a certain identity, which can help mold diplomacy and other issues, among those how they deal with civs of different religions. Certain civs would get a type of bonus for taking on religions that they would more easily be associated with. Certain religions may hate others, like Christian and Muslim. Then again there should be a chance they can work together for a time.
As you can see I have not worked out exact details, but it is a feasible idea. The civs do need something to identify themselves from each other, something I believe the game is lacking.
The other way religion could be installed in the game is through certain religious buildings (a building would represent a certain religion, if a civ decides to change religion it sells the old religious building and builds the building for the newly chosen religion), perhaps religious wonders (which could act like a national wonder from civ 4), these buildings would give that civ certain advantages in certain areas, perhaps disadvantages in others...
Heresy could be one, Catholics (during the Spanish Inquisition for example) believed ingenuity, or inventive, scientific thought to be heretic, so if you use Catholicism, there may be a hit to science, but a substantial gain to gold or wealth, or happiness (the selling of indulgences to get your aunt or uncle out of the hot place).
Whereas the Muslims seemed to go right along inventing new things, and rewriting the classics, studying science. Science could be their big advantage. Gold as well, perhaps coastal trade becomes a plus. The details need to be worked out, but I believe that these ideas are workable. Keep in mind these are just thoughts I have come up with, thinking and reading posts about what the game could use to make it better.