I definitely agree with some of your ideas Frekk though-as with The Cosmic Kid-I think fully customizable religions might be going a bit over the top.
Perhaps your original choice of religions is still out of a small group (Christianity, Islam, Judaism, Buddhism, Taoism, Shinto, Vodun (or Voodoo as its popularly known), Sikhism & Zoroastrianism come to mind-not Confucianism, as I don't view it as a proper religion), but you get the *option* to name your religion if you change one or more of your traits at any given time (perhaps with a limit on the number of times you can alter it between turns). All your religious buildings, though, retain the architecture of the original religion.
What is most important, to me, is defining the traits. As I see it, there are 3 major categories to look at-which I'll call "Strictness", "Secularism" & "Tolerance". Each category can be organized along a Left -----> Right axis.
Strictness goes from Fundamentalist---->Liberal (this primarily effects the chance of new religions being spread into your nation & the penalties any such religion will bring if it appears).
"Secularism" goes from Puritan------>Bacchanalian (this primarily effects the yields, commerces, happiness & health which can be generated from religious buildings-or the mere presence of the State Religion).
"Tolerance" would go from Sacrificial----->Ecumenical (would primarily effect yields, commerces & happiness relating to non-State religion cities, as well as diplomatic relations with civs of differing Sects/religions).
I agree that religion should be about penalties & bonuses. For example, adopting a Fundamentalist approach to Strictness, you might get bonus happiness & a reduced chance of other faiths spreading to your land, but you'd also get a penalty to science & a penalty to diplomatic relations with every other religion (& probably most sects of your own religion!)
Of course, this leads me back to the point I made earlier-that merely having same/different religions should not be the basis of your diplomatic standing. The various trait choices you make, coupled with your treatment of other religions within your borders, should be the primary "Religious" determinant of your relations with other civs.
Anyway, I think this approach opens up some intriguing possibilities. For example, you might be Christian & switch to Ascetic on the Secularism scale. Having an historical bent, you decide to rename your religion Catharism-then need to decide if you're going to be Fundamentalist & Militant or Liberal & Ecumenical-or something in between (just trying to imagine a Militant Sect of Fundamentalist Bacchanalian Buddhists-that could be funny
! Maybe some choices on one area should prevent certain choices in others? Or maybe not?)