Why is denying or promoting something considered hate?
Where is the list of things we are allowed to deny or approve of?
But they may also have no hate towards other ethnicities or desire their deaths. If pressed, they might even say that their vision of a "pure" society isn't worth the deaths of minorities that would come about if they tried to implement it.
I think too often we confuse the stereotypical example with the definition. The stereotypical white supremacist hates minorities, but the definition itself doesn't require it (I know of no surveys that would tell us what proportion of white supremacists match the stereotype).
My whole point is that you (and many others) are using a new definition of "hate" which doesn't match the old one. "Hate" used to be an emotion, a feeling, a dislike of something and a wish to see it destroyed.
One can feel superior to something without having any dislike of it or a wish to see it destroyed. I consider myself superior in many respects to the rocks in my back garden, but I neither dislike them nor wish them destroyed.
A supremacist may consider themselves smarter or prettier or taller than some other group, but that does not necessarily mean they want to destroy the other group.
Any left-wing should be allowed, any right-wing stuff should be denied.
Few exceptions exist on the western side, Spain is probably the most remarkable case. Reason why you wouldn't often hear much about what happens there, unless it is something negative to bash the right-wing people there.