-First of all, they were founded by witches with the purpose of uniting mankind under a new government, after the witchcratic system ended up failing to stop the demons in the previous war of the divine will. The original leaders were also witches, who wanted to reduce the standing of normal witches, to have it easier harvesting them and creating new special soldiers.
-They are aware of the existence of a God, but the key members aren't praying to it, and some members sincerely doubt about it's morality.
-Eventually the popes changed to normal humans, and in time, the excuse they used of witches being evil turned into something everyone inside the church actually believed as completely true (To the point that the "pure" witches grew up as crazy fanatics who hated their own kind, ignorant of the truth.
-The purpose of the church is preparing mankind to face the third war of the divine will, sadly, the division of the old witches, plus the fragmentation of governments in the barbarian lands, made it impossible for them to unify mankind in time, by the time the story takes place, they're extremely desperate, because far from being able to fight reliably the demons, even demonic beasts are dire threats to them.
-The harsh reality is that even their main plan, creating an army of judgement soldiers is a failure, since the ritual they use is incomplete.... and made so witches use those bodies.