This event is not in and of itself enough to justify calling them Nazis. The organizers themselves however have a long history with the more toxic aspects of the alt-right community. For example:
https://www.vox.com/identities/2019/7/1/18761623/straight-pride
While not necessarily Nazis in the literal, "They call themselves that" sense the event was organized by people who are players in groups who are ideologically aligned with most American Nazi groups. While calling them "Nazis" is a tad hyperbolic, it's a perfectly justifiable shorthand for describing their actual politics.
I'd say that's a rather large assumption given how small the parade was. "A few hundred" isn't that big, especially for an event that's been getting this much national attention for as long as it has.
The politics of the organizers have been at the forefront of a lot of that coverage. Anyone who marched in that parade either knew exactly who they were aligning themselves with or are so profoundly clueless and ignorant that they're among the sort who will happily go along with a totalitarian government as long as it says it hates the same people they do and shouts "Praise Jesus" every now and then.
If you want to be pedantic about it, we could call the marchers "Nazis, Nazi-sympathizers and useful idiots."