On Meta Stack Exchange, we have an editor tag with (currently) 440 questions, more than the minimum of 100 for tag badges to be awarded. We also have two users, balpha and Jeff Atwood who have a score of more than 100 and more than 20 answers, so they qualify for the bronze tag badge. Yet, they don't have them:
I suspect this is because they already have another bronze Editor badge. The tag badges don't exist in SEDE either, so it's not a display issue.