Longer if you count Dark Sun and Planescape.
Complete Priest's Handbook with full on non deity spellcasting specialty priests was 1990 and preceded both Dark Sun and Planescape.
"In the AD&D game, the God, Force, and Philosophy are identical in the way they are treated by the game mechanics. All three provide spells and powers to their priests. All three demand personal requirements and services of their priests and of their non-priest followers. And all three, to a lesser or greater degree, shape the world, both through their own powers and through their agents, the priests."
I think by core he means PH though.
Oe cleric class description did not mention gods, just Law and Chaos.
Clerics: Clerics gain some of the advantages from both of the other two classes (Fighting-Men and Magic-Users) in that they have the use of magic armor and all non-edged magic weapons (no arrows!), plus they have numbers of their own spells. In addition, they are able to use more of the magical items than are the Fighting-Men. When Clerics reach the top level (Patriarch) they may opt to build their own stronghold, and when doing so receive help from “above.” Thus, if they spend 100,000 Gold Pieces in castle construction, they may build a fortress of double that cost. Finally, “faithful” men will come to such a castle, being fanatically loyal, and they will serve at no cost. There will be from 10–60 heavy cavalry, 10–60 horsed crossbowmen (“Turcopole”-type), and 30–180 heavy foot.
Note that Clerics of 7th level and greater are either “Law” or “Chaos,” and there is a sharp distinction between them. If a Patriarch receiving the above benefits changes sides, all the benefits will immediately be removed!
Clerics with castles of their own will have control of a territory similar to the “Barony” of fighters, and they will receive “tithes” equal to 20 Gold Pieces/Inhabitant/year.
Doing a search for "gods" or "deit" on the OE first PDF I don't get any hits at all.