Though the modern white supremacist movement does also include a fair number of disenchanted military veterans [0], who are often influential in their organized groups and militias (and, the NSDAP itself included and was supported by a lot of other disaffected citizens that weren't “trained assassins”.) So, even aside from being dubiously relevant, the distinction you try to paint is at best overblown.
[0] e.g., http://taskandpurpose.com/nathan-damigo-charlottesville-mari...
Historically, all this folklore was a mean to an end. But the end came first. There was a plan to overthrow the government, a failed coup d'état, an relatable ideology, a strong, trained and motivated leadership, a propaganda, active enrollments and daily militia marching. In two words, actual politics.
Given their complete lack of all these, it seems to me very hasty and politically motivated to call these morons Nazis. Instead of dealing with these people for what there are - lunatics, it creates a fear for something that simply does not exists.
Nothing like these fucks then? https://twitter.com/SheldonKJordan/status/897795096325836804
EDIT This is not a qualitative comparison especially since my point is that both instances are not comparable.