There are three types of religions in the world. Universalizing religions. Ethnic religions. Traditional religions.
Islam, Christianity, and Buddhism are universalizing religions.
Judaism, Taoism, Confucianism, and Hinduism are ethnic religions.
Traditional religions is a generic term referring to tribal religions and religions that deal with spirits within inanimate objects or animals and such.
Islam, Christianity, and Judaism are all Monotheistic religions. The first monotheistic religion, according to some but not all scholars, was Zoroastorianism or something like that. Spelling is probably wrong.
Taoism and Confucianism fall under the category of philosophical religions, in that they make little or no pretense at defining deities and such, but they do have a religious aspect to them, making them different from thorough philosophies (which are more openly compatible with religions in general).
Hinduism is an extremely polytheistic religion, with over a thousand different gods. However, it is also a very fluid religion with many different beliefs within its practicing populace. In fact, some Hindus believe that the thousand+ gods are really just faces for one God, and that they are potentially compatible with the three monotheistic religions. The best demonstration of this, I think, is Sikhism.
Anyways, I think the current implementation of religion is fine as is.
Edit: I'm an evangelical Christian, so I'm biased. As it is, the current system in Civ IV is the least offending one to a religious person such as myself. I don't pretend to represent others, but in my case, I like things the way they are. Don't implement religious traits.