What's happening here basically is they're aware that the Left (correctly) refers to their movement as fascist, so they respond by saying "huh-uh, you're the fascists". Their "evidence" is basically that "socialist" is one of the words from which "nazi" is derived. And they think like "our voices are being unfairly silenced by the Left (also bullshit), and the Nazi's also didn't allow freedom of speech, therefore, the left are the "real" Nazi/Fascists".
They either have no idea, or do not care if they do, that it is factually accurate to say about that 90% of what THEY espouse is exactly what the Nazi's espoused (and the opposite is true of the Left), most of them don't want to be seen, at least not publicly, as little Nazis. They just want to say "I know you are but what am I", and the historical facts don't matter to them.
So, this is why they embrace a historically anti-fascist song like Bella Ciao.
It's also notable that the song appears in the video game "Far Cry 6", in which you play a freedom fighter against an evil dictator (who's referred to in the game as fascist) in a fictional semi-tropical country that has a lot of Cuban vibes, like it's something of a stand-in for it. The actual politics of the fictional evil dictator (played quite excellently by Giancarlo Esposito) are really never outlined, other than he's murderous, oppressive, and heavily involved in the drug trade.
They don't know history, they don't know that fascist = far right, like communist = far left. They think "fascist communist" is a pair of of words that make sense when combined, when they absolutely do not.