So, as I have said in my previous post, here is the summary of what OD&D suggests (more or less explicitly) on clerics and anti-clerics.
Clerics are part of a esoteric and military (1C) religious order (perhaps proselyte (6B)) characterized by its study of religious texts (2) enabling them to understand better the creation and get spiritually closer to their unique god. This exegesis of sacred texts gives them powers inaccessible to the profane (5). It's an hermetic society in which clerics progress through successive stages from acolyte unable to use the divine power (because she has to prove her worth) to the patriarch who guide the religious order and leads the Crusades, via the Lama doctor of the Law and the Bishop sent to the Wilderness to conquer his domain by the strength of his arm and the purity of his faith (2).
But as in any religion, strife await because of different interpretations of the Book : Any cleric who rises in the hierarchy of knowledge must eventually choose sides (1A) between the mainstream (the Law) which gathers most patriarchs and the deviant interpretations described as heretical (the Chaos). These are parallel orders* of Chaotic clerics (6A) more or less rejected by the Church of the Law, each led by a different (Chaotic) patriarch named heresiarch (7) which gathers also holy warriors (1C) and fight the undead too (4). Rather than building a fortress, they lead a nomadic life in as missionaries (7).
*for example : blog In Places Deep.
Anti-clerics are always Chaotic and evil (3). They are satanists* who worship many demons that are the source of their powers, counterfeiting the hierarchy of the Church of the Law (3). Evil High Priests also build strongholds for their respective cults (1) and are particularly civil with travelers who stop in their castle and pay their required tithes (6A).
*porphyre77 rightly pointed out that the pagan role was filled by Druids.
Any comment, guys?