I don’t know. I think Brownshirts fits better. They were the Nazis’ political paramilitary arm, known for attacking political opponents in street fights. They were also led by a gay socialist, Ernst Röhm. Antifa seems pretty “brownshirt” in its tactics and tolerance of opposing opinions.
I think most people think of Hitler’s SS, which was of course in charge of carrying out the Holocaust, when they hear “blackshirts,” rather than Mussolini’s street thugs. But since the Antifa terrorists often choose to wear black shirts, I guess they don’t have a problem with the association...