First off, I'd like to follow DrunkOnDuty's lead and also tip my hat to funkysnunkulator for his interesting and innovative posts. Little details like this can go a long way towards coloring a game and making it stand out.
I've been writing a series of articles on the gods of Greyhawk at Canonfire that touch on these kinds of questions-schisms within the faith, interaction of the church with outsiders, what is and is not a sin, etc. Far too often, it seems to me, official write-ups of clerics have them doing everything from acting as farmers to judges to playwrights and performers-that is to say, everything BUT what is typically associated with priestly duties: preaching, confessions, exorcisms, blessings, marriages, counselling, communing with higher spirits, etc. They have secular jobs with priestly powers.
A few general notes:
-Very few faiths of any sort are entirely homogenous. Just as it is foolish to depict churches and religious faiths as being entirely homogenous blocs whose members all think and act alike, so too is it wrong to think that all fantasy clerics are on the same page. You don't have to be secular to be an intellectual-theologians like St. Augustine, Peter Abelard, or Thomas Aquinas, or some of the Islamic scholars of the Middle Ages, all made important philosophical and intellectual contributions. Who says fantasy clerics can't do the same?
We all know the various divisions within the Christian faith-Catholic, Protestant, Methodist, etc. But it's also worth noting that Islam has divisions and conflicts of its own, most notably between Sunni and Shi'ite branches of the faith. I don't know as much about Oriental religions, but IIRC there are different traditions of Buddhism-Zen Buddhism versus Taoism, for example. These rivalries are not necessarily hostile-intellectual debate and discussion is a regular feature of the fantasy religions, and they change and evolve with time, just as theology, philosophy, etc. do in real life.
-Not every church has a big political agenda. Some of them do, of course: PC clerics and BBEGs are commonly the most active and outgoing members of the faith. But others, even within the same church, are more interested in giving sermons, officiating at funerals, offering blessings, conducting ceremonies, and the hundred and one other things priests do or have done in the real world, without risking their hides in the wilderness. But, again, not every faith has deep socio-political comments on the world, and their priests don't actively meddle in politics in their day-to-day activities.
-Good and evil aren't always as clear-cut as they seem. Evil temples can openly operate in cities like Niole Dra or Greyhawk, usually staffed by more moderate clerics who are more concerned with acting in their deity's areas of concern than hatching evil plans to destroy the city. A priest might be of Chaotic Evil alignment, but that doesn't mean he's a moustache-twirling villain out to destroy the PCs; rather, he adheres to a sect that doesn't actively preach destruction and depravity.
His personal beliefs might be those of a nihilist, who believes laws to be worthless creations of humanity that will rot and die along with the people who created them, but he doesn't go out of his way to break them, either. More interested in fulfilling his religious duties than in making a political point, he simply flips off the city watch behind their backs on his way to the market to buy food for the beggars who come to his sermons of death, gloom and misery. He might believe that life is a futile and miserable thing, but his branch of the faith doesn't teach that it is his responsibility to spread misery in his god's name. As such, evil churches can just as easily operate in good-aligned cities and lands.
Similarly, good-aligned faiths can operate in evil lands, as well. They might believe as strongly as possible in equality and fairness for all, but they are pragmatic enough to realize that they can't possibly fight and defeat the oppressive forces that rule the land. Hence, they stick mainly to caring for the poor and sick, to make their otherwise miserable lives a little easier. Challenging the authorities will only get them hanged or impaled, and then who will take care of the poor and the orphaned? The authorities might not be overly fond of them, but they know that the priests aren't going to challenge them, and their feeding the poor gives the rabble a bone or two to keep them from revolting.