Antonyms include valorize (in American English) or valorise (in British English), exalt, extol and acclaim (all transitive verbs), or pay homage (intransitive, but can take to and an indirect object).
I think these are particularly close antonyms because they all mean attempting to raise someone’s reputation, but valorize is the closest because the subject of the verb does not have to be a person and it does not imply a speech-act.
Take, for example, the sentence, “Memorial Day valorizes America’s fallen troops.” That’s the closest antonym I can think of to a phrase like “stigmatizes Vietnam veterans.” The word exalt would also work, but doesn’t sound as good to me. It would be incorrect to say extol or praise, because those are things only a person can do. We can stigmatize through our actions or by implication, but acclaim or praise is more specifically a speech-act. We could also say honor or pay respect to in this context, but those are broader: they could also be things we do in private, and stigmatize necessarily means damaging someone’s public reputation.
If we say glorify here, that connotes undeserved praise, in much the same way that stigmatize connotes undeserved oppobrium, so in one sense it’s a better antonym, and in another, a worse one. Interestingly, honor is the only one of those words that specifically implies the person receiving the homage deserves it, but I can think of many others that carry the opposite implication.