What class would a priest be who believes and preaches something that does not, in fact, exist, like Tummyachos, the god of too greasy sandwiches? Cleric? Of course he wouldn't receive any spells, but I don't care.

Cleric, if they actually spent a lot of time preaching dogma, converting, and/or truly believe the thing exists.

Any class can rant about false gods though!