Both sides will claim that the other side is fascist, because calling something fascist is a powerful rhetorical tool. Still, it's possible for one side to be correct and the other side to be incorrect in their characterization.
It's really only the most mindless middle school name calling of the last two years or so where you get Trump people saying "oh, but it's national socialist" and now Putin. It's trolling, "flooding the zone with shit". The Nazis were better than that.
That's because they (and their Italian buddies) hadn't yet etched in world consciousness the image problem fascism and Naziism has that such attacks seek to leverage.
They did accuse their enemies of being all of the (often mutually contradictory) equivalent boogeymen of the day, though.