This actually sounds interesting... What if religions had some kind of bonuses or special mechanics? Perhaps ones to chose depending on what kind of faith you want?
It wouldn't need to be D&D-esque with all kinds of magical powers. Civ5 does give an interesting mechanic for religion, and it's all pretty neutral and mundane.
That's not a bad idea. How about something like this:
Let priests have significant influence over the peasants who believe in their faith? At low levels, they could nudge morale and loyalty up and down. At higher levels, it might be reasonable to give them the ability to raise up a peasant mob to kick Lords or knights out of their estates, or even (if the priest's skill is high enough, and there's not enough troops in the region to stop it) claim the region as a new outpost of the religion (naturally, giving the priest the lordship in the process!).
...Hey, wait a second....
