Religion has had many forms during the history, and those may have been even more influential culturally than any particular religion. For example, most Indians and the ancient Mediterraenean civs (Greeks, Romans, Egyptians...) had polytheistic religions of multiple gods dedicated to various aspects of life. Some cultures on the other hand have raised their mortal leaders to the position of gods and worshipped them as such - for example the Chinese and Japanese, or again the Egyptians and the South American Indians. Then there are the "modern" single-god religions such as Islam and Christianity. Further, in some cultures philosophical teachings took the place of actual religions - I guess Confucianism would fall under this category. Then there is of course the option of Atheism.
These religion types could be introduced in the place of the named religions or even as a new civic option. You could have your religions as they are now, but you'd also be able to choose how they are practiced - imagine polytheist Christians or Judaism that worships the Emperor as the God's representative on Earth. Religion types as civics would also allow the characterization of the religions without offending anyone, as religions could still remain neutral while the religion types would have various traits.
For example, Polytheist religions could have a culture bonus, while religions worshipping the Emperor as a god would be more obedient and Atheism would give a small bonus for science while suffering a culture penalty.
These religion types could be introduced in the place of the named religions or even as a new civic option. You could have your religions as they are now, but you'd also be able to choose how they are practiced - imagine polytheist Christians or Judaism that worships the Emperor as the God's representative on Earth. Religion types as civics would also allow the characterization of the religions without offending anyone, as religions could still remain neutral while the religion types would have various traits.
For example, Polytheist religions could have a culture bonus, while religions worshipping the Emperor as a god would be more obedient and Atheism would give a small bonus for science while suffering a culture penalty.
