Yeah, this is an issue I have with this approach. because if a demon lord is wrecking chaos, I want to know which Powers would be interested in helping stop them. Yes, I could say "any devil will lend a hand stopping demon lord....for a right price" or "Any celestial will gladly join the battle against the forces of evil" but that is boring and generic, I feel adding more personal spite between the individuals adds more spice to the story.
I am pretty sure War of the Seldraine, Lolth's banishment and her usurping of Ghaunadur to gain godhood rely on Realms-specific gods that do not exist in Greyhawk or other settings with Lolth, for them to be canon in other worlds.
Just did a real quick glance. The Forgotten Realms definitely goes into more
detail than other settings, and tries to make some more explicit statements about how/where multiverse lore intersects with the Forgotten Realms history and personages, but the Elder Elemental Eye originated in context of Greyhawk lore first, as did the idea of Lolth as a rebel member of the elven pantheon.
And the various Forgotten Realms gods
do exist in the same D&D multiverse, since those worlds do. Obviously people on Oerth don't know about gods that aren't worshipped there, just like people on Faerun don't know about gods that aren't worshipped there. But they all exist in the same multiverse. This was all explicit since at least the dawn of 2e, when Spelljammer came out and the Forgotten Realms setting was young, and it was developed in much more detail through the Planescape material, that actually gave us information about rivalries and alliances between gods of different pantheons. And in the Forgotten Realms case, they have gods that explicitly are also part of other pantheons that exist in the D&D multiverse (Tyr, Oghma, Meilikki, etc, not to mention more explicitly multiversal and D&Dish ones such as the Elder Elemental Eye).
In 3e, there was an attempt to make each setting exist in their own own entire multiverse rather than being worlds in the same Material Plane, so if you go with that (which was reversed in 5e) you could say that the various Lolths were different beings or dimensional "instances", but that interpretation doesn't appear to have been empasized in 3e cosmology. There was an apparent attempt to keep most of what was going on (other than planar arrangement) consistent.
In the enormous amount of published Forgotten Realms material in 3e (and certainly 4e, but much of 4e lore actually does have to be treated as a different multiverse because of its general departure from a continuity that was partially retconner in 5e) by multiple authors there are undoubtedly mentions of lore bits that are inconsistent with the greater multiverse lore, but these are exceptions rather than the rule, and are going to be primarily regarding minor details rather than the major players shared multiverse history.
What happened was that Forgotten Realms over took the other setting in popularity and published material during 3e. This is also when Eberron was introduced, in context of it being in an entirely different multiverse (so its lore was unrelated, Marvel to DC so to speak).
Jump past 4e, which used lots of previous lore but did its own thing, and 5e introduced things like MtG settings in D&D, which don't neatly fit into the existing lore. So, despite 5e's explicit return to the multiverse and Planescape, players come into the game where they are familiar with: Forgotten Realms, Eberron, and Magic the Gathering worlds, all of which have very distinct multiverse lore (even though 5e absorbs Eberron into the Planescape multiverse, and even the MtG settings, without really telling us how that latter one works).
And because there hadn't been a lot published in the past decades regarding the multiverse in context of Greyhawk, Spelljammer, Planescape, (or even other traditional multiverse settings like Dragonlance, which also existed in the same multiverse, despite minimally interacting with the shared elements) when they think of the elven and dwarven pantheon D&D pantheons, or the demon princes, or the City of Brass, the only place they saw them was in Forgotten Realms products, not Eberron or MtG, so they are just "Forgotten Realms lore".
We therefore have this (completely understandable) misunderstanding, which I attempt to correct at every opportunity, because it prevents people who might be interested from realizing there is a greater depth and connection of D&D lore out there than they realized. Once they know that they have the opportunity to really dig into the whole Planescape+Spelljammer history and greater multiverse setting if they want to. The mistaken idea that these content elements are Forgotten Realms specific things tends to dissuade this curiosity and thus awareness.
