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.
Because anyone call themselves anti-fascist, doesn't make them so. While most people who are, well, not fascists probably don't wear or care about the label. You basically confirmed the point of the comment you replied to.
> I’m sure there are supremacists “organizations” that are also hard to pin down.
You mean the ones that aren't organizations? Let's say all the people who are racist in the world, are they an organization? Even all the people who really hate the same "race", if that's all they do, does that make them an org? Is everyone making inane arguments be part of a global group of people working in concert trying to diminish the cognitive capacity and level of discourse in society?