Non-leftist doesn't equal right-wing. Anarcho-capitalism is right-wing, but opposite from fascism.

Fascism requires no logical structure and no coherence in ideology. It requires the ideology to be bendable all ways each moment for each different situation. Which, well, is natural for an ideology reliant upon violence and emotion above all.

That leftists try to mix fascism and normal conservatism is a purely leftist sexual problem, that doesn't concern others until leftists pretend it's commonly accepted.

Then, of course, when most of the "revolutionary" competition is leftist, fascism becomes anti-leftist and allies right-wing forces.

But also Nazi and Soviet propaganda on the British Empire were amazingly similar in archetypes and emotion. Which would be a rare case of "fascism against right-wing forces".