Note that, in the abstract, “vulgar” means “common” (as in “vulgar latin”). Indeed, its negative connotations come from that same sense: “common” people are unrefined.
Yes, in Spanish vulgar is used as inappropriate. We have "el vulgo" (el pueblo, the people), which kinda teaches you the correct meaning, popular, unrefined. But "vulgo" is seldomly used.
This goes pretty deep in English. I'd argue that the semantic intention behind the colloquial usage of "vulgar" is nearly inseparable from the "class distinction" baggage it carries. Consider these common synonyms and their etymologies:
And even synonyms like obscene, indecent, or disgusting, which don't evoke this distinction directly, still almost always ultimately rely on separating things based on what is "good" and "clean" according to class distinctions.
