Old world tabards still work, at least some of them, but it’s idiosyncratic.
You can put on player racial tabards from Vanilla and blast through TBC or Wrath (or Cata? can’t remember) dungeons to speedrun rep.
The best thing to to is to check exactly what works for each one. Hit up wowhead.com and search for the faction in question, and read the section on “How to earn rep” and read the comments - the best stuff on Wowhead is in the comments!