"offensive or socially unacceptable or disgusting or wrong or criminal"
Those are very different things, and often subjective, by individual or by society. That I find something disgusting doesn't mean it is, or should be, socially unacceptable or criminal.
This site is dedicated to girl/girl love, which has been considered all of those things.
And 'problematic' can mean "I like something because of something that would harmful/wrong in real life" (rape fantasy, say) or "I like something despite its problems, which it would be better without", like Lovecraft and racism, or possibly Kase's controlling jealousy in this manga. (Though latter might be the first problematic for someone!) Can also mean "there's some sort of social acceptance flaw here but it would take more words than I want to spend to say exactly what, so I'll just use problematic and move on".