I see no reason why hate is not an appropriate term for that animating force which is compelling a mob towards vigilante action against a perceived wrongdoer -- a perception certainly rooted in racial bias. In order to get to the point where a lynching is possible, a person who cares about justice, law, order etc must convince themselves of the victim's guilt beyond all doubt. If the victim is already nearly subhuman to you, it's much easier to convince yourself that there's no moral risk in making the wrong judgment.
Just think about it from your own perspective: how certain would you have to be of someone else's guilt before you would feel comfortable attending their impromptu execution? If some neighbor came to you and said "we're gonna kill this guy, I heard he raped someone," you certainly would pass on that, if not stand up against it.
If we take away the hatred, what you appear to be saying here is that lynchings are well-meaning attempts at justice, which are inappropriately realized. This is silly, at least, to anyone familiar with the history of lynchings.