It would be more precise and more common to translate literally, as a noun instead of adjective, since it's a noun in Ukrainian. Therefore, an article is necessary before the noun.
She is a vegetarian.
It is a noun is Ukrainian, but it is an adjective in English. So we don't need an article here.
It is either a noun OR an adjective in English. It is used as both, but more commonly it's a noun in English too, describing a person. The adjective is used to describe food. For example "this is a vegetarian recipe."