In case people are still wondering why moderates don't like the idea of "Antifas" going around punching "Nazis", I found this illuminating passage about the Berkeley protests :
https://en.m.wikipedia.org/wiki/2017_Berkeley_protests
So, the way I see things, both Antifa and Neonazis like to beat up immigrants and people who "look wrong".
The protests continued for several hours afterwards, with some protesters moving into downtown Berkeley to break windows at several banks, a Starbucks, a Target, a Sprint store, and a T-Mobile store.[8][6] Among those assaulted were a Syrian Muslim who was pepper sprayed and hit with a rod by a protester who said "You look like a Nazi",[9]and Kiara Robles, who was pepper sprayed while being interviewed by a TV reporter.[10]
https://en.m.wikipedia.org/wiki/2017_Berkeley_protests
So, the way I see things, both Antifa and Neonazis like to beat up immigrants and people who "look wrong".