An aspect of Religion in Society would make it very flexible, especially with the ones we have in reality.
Christinaity, Islam, Buddhism, Jewishism, ecetera.
However I agree on allowing players in an circle to establish an religion. Especially the influence Religion should have upon players empires whether they're not that religion or not.
When it comes to be 'cautious' and 'careful' about religions in games, how sensitive is it really? Civilization 4 is very unique and much more interesting with this aspect as it allows domination type games, more abilities, unitation or 'holy wars'.