What exactly would happen? You really think that the events in Charlottesville were because of Hitler? the KKK predates the Nazi party by over half a century. Eugenics was considered a progressive theory in the late 19th and early 20th century.
Anyone who simply defines the protestors as Nazis is either intentionally pushing a hyperbole or is negligently oversimplifying the situation.
Secondly, I tend to agree that the term ’Nazis’ is... inaccurate. Deserved, earned, maybe even desired by the paraders themselves but fundamentally inaccurate. They synthesise their ideology down to a kernel of intolerance and racism and reach the conclusion that they are the natural successor in an unbroken line of descent from the ’cool’ Nazis, and thus they claim and are accorded the mantle. However national socialist ideology was far more complex, and the Nazi party's structure far more evolved, than these little folks have.