I'm A Banana
Potassium-Rich
Oh. I guess we have differing views on what counts as "campaign specific"; I've always seen the story of Correlon putting out Grummush's eye as being a generic, universal story true in every campaign setting where elves and orcs exist. (The 2nd edition book "Monster Mythology" basically says as much.) What I mean when I say "campaign specific" is stuff like "In Ebberon, halflings ride dinosaurs" or "In Dark Sun, halflings are cannibals", whereas a statement like "The halflings worship the goddess Yondalla" I consider generic.
See, statements like this, and folks wonder why I harp on about the Default Effect so much.

In reality, of course, "halflings ride dinosaurs" is no more campaign-specific than "halflings worship Yondalla" (debatably, less!) or even "halflings live in cozy burrows and enjoy pipeweed and gardening."
EVERY kind of halfling is really a specific kind of halfling. Those treated as presumed in various e's of D&D are just a specific kind of halfling that has been privileged above others by being treated as the "default" (making everything else a "variant").
Which means it involves some effort to change what "halfling" means in your game, as you work against the default assumptions of whatever edition you're working in and any natural resistance to change your group might have.
5e, FWIW, mitigates this by using subraces. While it still exists to some degree, it's easy to understand that your homebrew world has its own "subrace" of halfling that has its own story.
Of course, it doesn't look (so far) like there is such a mechanism for those who don't want 5e's default cosmology. There is a privileged cosmology, and everything else is a "variant," an "homebrew," some sort of lesser, less important, less relevant cosmology.