This is a rather touchy subject for me, and is what long ago inspired a "no real world religions" rule at my games. The reasoning is that most of the people I game with come from a wide variety of religions and beliefs, and some of these individuals take a dim view to having their gods or religions butchered in some game.
In addition to that, I have some players who will not, under any circumstances regard certain religions positively(xtianity tends to have a pretty piss poor reputation, and tbh, that rep has been earned) and refuse to play in a game where such faiths are regarded as positive.
What I have found that seems to be "ok" with most players is weak caricatures or facsimiles. If you make enough changes(#s of deities, names, overall belief system) you can keep political structures and 'rules' intact.
In my current campaign, the Western Imperial church a weird amalgam of the Medieval Catholic and Eastern Orthodox churches(as best as I, a modern heathen, can understand them) with multiple divinities. This seems to fit the standard cleric class just fine(and has the added benefit of not ticking anyone off). I'm not allowing the Cleric class to work with any of the other human faiths.
Thankfully, 2nd edition has a plethora of options for building priests of other faiths. The PHB, the DMG, and the Complete Priest Handbook are all useful tools for this type of class construction. In addition, there are a ton of different priestly classes already present in the 2e library(Crusaders, Monks, many different types of Shamen, Druids, Specialty Priests, Rune Priests, and others).