I'd love to include the ability to "customize" your religion, but I think this is better left outside of the current discussion as a future feature.
I can see why a fully customizable religious system would be too far-sweeping for this discussion, but what about an interim measure, a religious system that offers choices but isn't fully custom-built? The idea of allowing nationalized variants of major religion could be carefully limited to only a single variant -- when Protestantism is founded, civs that adopt it are offered the choice of founding a national version (like Anglicanism), but that option is no longer available after the first civ to do so. There would be costs and benefits, so it wouldn't be automatic or an obvious choice, but it would allow a diversity of religious choices as reflected in the real world.
A few examples of such national variants:
Hinduism --> Ayyavazhi or Bahkti (Tamil sects/schools)
Buddhism --> Shinto (Japanese syncretism)
Islam --> Shi'a (predominates in Persia/Iran)
Catholicism --> Uniate Abyssinian Church (Eastern Rite in Ethiopia)
Orthodoxy --> Russian Orthodox Church
Protestant --> Anglican Church
And of course, if we decide to make Pantheon a religion rather than a religious civic, there are all kinds of nationalized variants.
I suppose the bigger question is: how intensive are religions in terms of the Civ IV engine? Are there limited number of slots, as with civilizations, or is adding a new religion more comparable to adding a new building or unit that can be produced? How much lag does each new religion generate?