Nationalism is not left or right. Anti-gay sentiment is cultural ideology, not political framework. Authoritarianism and socialism, strong centralized government, these are leftist tenets. Black block vs brown shirts was leftist power struggle. The nazis allied with the soviets at the start of WW2. The communists, the "national" socialists and the fascists were all on the same side at the outset, against more socialists (brits) and a socialist president later (FDR).

You think leftist groups won't fight eachother? Or that one leftist group opposing another makes them right wing, or tolerable to the right?

You don't understand political systems at all.