Fascism is stridently nationalistic, whereas al-Qaeda in particular is definitely not nationalistic. If it's not nationalistic, it by definition cannot be fascism.

Anti-Semitism is not a defining feature of fascism, though it's certainly a good indicator. The original fascists under Mussolini were plenty aggressive, militaristic, totalitarian, etc before they became anti-Semitic.

And Communism was also totalitarian and frequently aggressive and militaristic, but we don't call them "commiefascists" because that makes no sense.