How are they winning by being ignored? If they're trying to solicit attention and anger from you, cutting them off by proverbially shutting the door on them sounds more like they lost.Yes and no. If you have to ignore them, they win. I won't allow that so I don't ignore anyone.(though I think some have ignored me for pushing back).
Its all up to the person and what they can deal with.
But besides that if they're being toxic why we worrying about their feelings on the matter?