[We should condemn their ideology through starvation of attention, not silencing them.]
The problem is that doesn't work.  The US tried that while WWII raged in Europe and Asia.  That's the problem I have.  I agree with you that speaking hate is not the same as acting on it but I cannot deem it "peaceful" if it's very purpose is to disrupt the peace and spread such beliefs to others.
[Regarding white supremacists, my take was that he lumped ALL of the "whites first/whites only" groups as "white supremacists."]
So why do you think Trump said, "some of those people were not white supremacists by any stretch?"  He made some clear distinctions in regards to the protesters that I just cannot fathom how he reached.  They somehow "wanted to protest the taking down of a statue Robert E. Lee" but the only plausible reason is because of glorifying what Robert E Lee stood for, ie. defending the slave trade in the seceding US states.
[erase our history]
Is that erasing to just not glorifying?