Yes, they did that in 1st and 2ed game. For example the goddess of magic in Forgotten Realms:I didn't know 1st and 2nd ed did that with cleric alignments, I could totally use that.
EDIT: what about a neutral cleric rejecting the temple's teachings but still having the power? (in this demiplane, you're born with magic, divine or otherwise. yay spontaneous casters) That could work, just deny access to domains.
1st Goddess: Mystryl, CN, clerics could be any aligment
2nd Goddess: Mystra, LN, clerics could be any lawful
3rd Goddess: Mystra (Midnight), NG, clerics have to be within one step, older cleric are grandfathered in.
Complete Divine has the Ur-priest PRC. I would use this as a model for the clerics who reject the gods. At minimum they should not get any domains and are hunted by the clerics of both gods.