All officially released resources such as printed books (like PHB, MPMM, ERLW, MOT, VRGR, XGtE, … ) and material officially released for Adventurer’s League (like ALCoS, ALEE, ALRoD, …) are allowed. You can use stuff from all these resources without restriction. You cannot use playtest material (such as Unearthed Arcana), homebrew and 3rd-Party materials.
so as @Arthilas correctly stated, the Explorer’s Guide to Wildemount (e.g. Echo Knight fighter) would be fine Call of the Netherdeep would also work at any table (e.g. if a DM wants to drop a magic item from that book)
on the other hand: Tal’Dorei Setting Reborn (e.g. College of Tragedy bard) would not be fine
… unless a DM allows it as a Homebrew Award … sadly such a character would not be playable at other tables
Main problem would be such a character would only to be allowed to play at your table … which would defeat the purpose to be able to play your characters at any V.A.L.U.E. event.
… same would be true if a DM would allow a player a homebrew race or subclass
Ihmo adding homebrew spells that only work at your table is a far easier, since such a character can still play (without casting such spells) somewhere else. (examples here and here)