Neo-nazi, probably. If someone LARPs as a 1920's gangster I am not going to say they are part of Capone's gang.
I guess I have a strong aversion to calling similar ideological bents specific groups from history. Modern socialists aren't Bolsheviks. Racist skinheads aren't Nazis. Violent Catholics aren't Crusaders.
Mostly because of the major difference between talking shit and literal murder.
