Even Greener Pastures

Interesting question, Nikola!

Just my two cents: "She's a gay" really stands out to me as awkward, if not downright wrong. That's something I'd never say.

As to vegetarians and vegans, I think it used to be correct to use the words as nouns when talking about people ("s/he's a vegetarian/vegan"), but I've heard/seen them used without the indefinite article so often by now - perhaps it doesn't matter anymore?

Technically speaking - but don't take my word for it, my German may be interfering here! - I think you could take "she's vegetarian/vegan" to mean that she doesn't contain meat/animal products, couldn't you?

At any rate, that's the way it works in German: Probieren Sie doch die Frühlingsrolle, sie ist vegetarisch. (Do try the spring roll, it's vegetarian.) vs. Ich esse kein Fleisch, ich bin Vegetarier/in. (I don't eat meat, I'm a vegetarian.)

Which - sorry! - automatically leads me to the intricacies of German orthography and pronunciation: Er ist Vegetarier (He's a vegetarian) vs. Er isst Vegetarier (He eats vegetarians) 

Edit: There's a - pretty short - discussion about this on wordreference.com:

vegetarian or a vegetarian?

The context is the following: My sister is....; she doesn´t eat any meat or fish. Can we use "vegetarian" as an adjective or do we need the article "a"? Thanks

WordReference Forums · forum.wordreference.com

tl;dr
Some native speakers seem to think both are fine, while others are in favour of using "a vegetarian/vegan" for people.