I can't back it up with rules, but for me it would be natural for me to say he's vegan, he's a vegetarian, he's gay.
Ha! That's just what I was thinking. Vegan, a vegetarian, gay. Indefinite article in front of vegetarian, but not in front of the other two. I have no sensible explanation for this. I thought that maybe my non-native intuition was playing tricks on me. 
Your non-native intuition is in agreement with my non-native intuition, although I have been torn between "vegetarian" and "a vegetarian" at times but that was probably because I wouldn't say "a vegan" and I assumed they had to follow the same pattern. It's very strange indeed. Could it be because a vegetarian is less likely to be mocked for who they are? Just a thought.
Mmm... Maybe... My hunch was that it was simply because
vegetarian is a longer word than
vegan. But maybe I'm totally off.
ETA: Another possibility is that it's because
vegetarian ends with
-ian. It's a little bit strange to use
-ian words as adjectives (not impossible; just a bit unusual). Does that sound plausible?