To be frank, I don't care much for what goes on the mind of white supremacists. Their thought process is obviously corrupted - otherwise they couldn't hate other human beings for such superficial reasons.
Look, the reality is, there would have been no BLM protest if their hadn't been an armed white supremacist march. One side started everything. One side came heavily armed. One side murdered. That a few people on the other side may have thrown a few unprovoked punched bothers me less than not at all.
I do care how they present their argument because their movement is gaining traction to the point they have a representative in the White House along with a number of his staff.
Their minds may be corrupted, but we have good normal people who see their point (like the few of us on this thread) and that's unfortunate. To this day the Black Panthers and Malcolm X are maligned where MLK isn't. Think of the reason why.
When fighting an oppressor it's important to not resort to their tactics. Think of the Palestine/Israel conflict for example, if the Palestinians would resist using a peaceful solution, they would get a lot further because almost everyone is against Israeli demolishing of Palestinian homes... but the minute they strap a bomb to themselves, no matter how justified their anger at being displaced, people don't want to side with them.
I don't think punching nazis and fighting them on their own level does anything but allow them to justify their distorted sense of reality. I think real change comes when you're better than that which you claim to hate.
Think Ghandi, Nelson Mandela, MLK.