Only by the creators and audience. That’s what makes them not Hate Sinks.

Yes they can. Jonah Liebert is a good example.

@Ditb01 that’s literally everyone

You should choose your words more carefully

How about Griffith/Femto from Berserk

Yes, a villain's horrendous actions don't automatically make them one dimensional. Sauron, Morgoth, Johan Liebert, Hans Gruber, DIO, The Major, Shogo Makishima, Anton Chigurh, Vicious and Albert Wesker are great examples of this.

Yep

Yeah obviously, if written carefully. In terms of characters I'd add to this discussion as examples I'd also include Akio Ohtori and Emperor Belos.

Even three-dimensional villains can be pure evil and totally unsympathetic. Usually, they would fall under fake tragic but all of them.