> If so, why carry those flags and bandanas on their faces?

The flag just symbols that this person is against Nazis. Nothing more, nothing less.

It can be held by anyone. Here in Germany, we have (amongst others, just a list of what I have seen) religious Christians (often of Lutheran Protestantism), Marxists, Leninists, Stalinists, other denominations of Communists, Anarchists, Greens, Social Democrats, Antiimperialists, Zionists and sometimes even the occasional Conservatives showing up under the Antifa banner.