If I recall correctly, there is a limit of 3 badges that can be shown (admins/staff might exist outside of this) .
The first slot is ‘reserved’ for Moderation status, second slot is ‘reserved’ for subscription status, and third slot is ‘reserved’ for “other” (As in, turbo, cheering, or Twitch Prime). The slots may not be in that order in chat, but I believe that’s how its set.
That limit may be in place in order to reduce chat spam (everyone having 3/4/5+ badges? Crazy.) When they had the Horde/Alliance badge as a promo for the Warcraft movie, it replaced the Turbo badge.