Yes, labelling a person who disagrees with you Nazi seems like a perverse application of Godwin's Law. It means you are intentionally ending the discussion. Why do it?
That kind of nuclear option rhetoric wise allows them to feel empowered both by denouncing an enemy and creating a call to arms within themselves and others. Furthermore, even if it antagonizes you, it draws you into their struggle, which legitimizes their world view. It creates a threat for them to fight against. If their rhetoric causes someone to radicalize to the other side, even better. It just strengthens the immediacy of their cause.
This is how Antifa and Neo-Nazis can have a weird kind of symbiotic relationship. Even if their methods don't recruit someone to their cause, forcing that person to become a part of the overall struggle legitimizes their world view, strengthening both parties at the same time.
Which I found disturbing, but I don't see how it makes him a Nazi.
The police seems to have effected a policy that all but necessitated a violent confrontation, by forcing the alt-right protestors to move through a large hostile crowd of Antifa protestors on the way to their new location, and the police not protecting the alt-right protesters.
There's more strange things that happened that day, but was there any official explanation why the police officers were ordered to use these unusual and harmful tactics?
This is why people call Trump a Nazi.
Portraying the whole alt-right (or the whole right) as Nazi's is inaccurate, offensive and divisive. It just helps them, and it leads to everyone reasonable getting stuck between angry fascist communists and angry fascist Nazi's.
As an aside, white supremacy != Nazism. Nazism includes white supremacy, but adds some other factors like fascism. White supremacy is not all that different from the popular Jewish supremacy movement in Israel. Most peoples want to preserve their cultures and not let themselves be replaced, but it seems like only European welfare states and the U.S. are ever attacked for it.
When did you last hear about the "Islamic supremacy" that is the dominant culture in the Middle East?