Not commenting at all on the whole gods debate, but,
@Azzy is right when it comes to 1e and 2e.
The notion of "Core Rules" was a 3e invention that didn't exist in AD&D. In AD&D, ALL RULES were core, except those that were specifically called out as optional. Thus, you see Barbarians (as the class) being used in 1e modules like Isle of the Ape. Rules from various, what is now termed "splats" appeared and were referenced repeatedly by later publications.
The Wilderness Survival Guide (to pick an example) is every bit as core as the Player's Handbook in 1e. As is Unearthed Arcana. The Complete Guides in 2e were also just as core as the Player's Handbook. You were presumed to be using them. Heck the books often referenced each other.
Only setting specific books were truly optional.