Well, vanilla classes are not quite defined. The basic four are part of it, with their subclasses as in the basic rules, at least i would say that. On top of that? Ask a Grognard and he would answer: why do you need more? Ask someone who grew int othe game with 3e + and he would say: each class and subclass in the PHB.
Still, vanilla is normally not defined so much by fluff. What is vanilla these days anywhere? 2e greyhawk is kind of vanilla, 2e FR eventually also. Dragonlance? It looks vanilla but i would say it is not, to much extra special rules.
Some classes require more backstory fluff than others:
Example:
a cleric can be basically played without church and does work perfectly without deities, purely following a principle (good/ light / evil etc.)
A druid normally requires druid circles, forests etc. etc. Still e.g. Darksun tied them to elemental specialities in the landscape e.g. a (water-) oasis.
A fighter is most universal (except EK).
A rogue comes second to it (except AT).
A mage reuires magic to exist in your game world.
A sorcerer? According to PHB there has to be either wild magic or dragons present in the campaign world.
Whereas as pointed out a cleric does need no "patron", a Warlock does need one.
Bang, you need some other planes or other mystic thing going on in your campaign so a lock does function.
Ok let us go on, Ranger, hm would basically work on its own.
Paladin hm eventually yes but it is tied to some ethics or codex so such things must be there. Would not make much sense in a very uncivilised setting.
Barbarian? That is also a cultural thing somehow, it requires some tribal or primal culture otherwise it is a lot of shoehorning. You do not believe me? Imagine a modern setting and try to define a meaningful barbarian.
Monk requires order, religious/philosophical organisation, so no except some hermit or so.
A bard? Cultural and best high culture required, at least plus it needs magic.
So, i hope i did not forget anything.
