The point is that the Nazis were motivated by an ideology of racial supremacy, and that this was a significant factor in triggering WWII. This isn't some kind of wacky revisionist history I'm putting forward here. Look at any historical account of the Nazi invasion of Poland (which of course precipitated WWII) and you'll find "Lebensraum" mentioned quite prominently.

You can argue that the use of the term "white supremacy" is anachronistic in this context (as the Nazis were technically "Aryan supremacists" rather than white supremacists). But the current white supremacy movement has evolved in significant part from Nazi ideology. Take a look at the Wikipedia article on David Duke, for example, and you'll find such statements as "Picketing and holding parties on the anniversary of Hitler's birth, he became known on the LSU campus for wearing a Nazi uniform."

In short, if we're talking about racist movements within the US and Europe that are directly inspired by Nazi ideology, then whatever quibbles you might make about terminology, you can't deny that it's reasonable to project the dangers of the latter onto the former.