It really is peak absurdity. Mussolini's fascist party, which he founded and from where the name comes from, goes on to exist as "MSI" under his supporters and now under the "brothers of Italy" moniker with basically a veneer on old policies to make them more palatable but you call a spade a spade and the ahistorical, unread deplorables get triggered. It's like saying the KKK is not racist basically.
In speaking of Italy and Germany leading up to WWII, it boils down to authoritarianism and totalitarianism. Both dictators cancelled any other political party. At that point it doesn't matter they allow corporations to maintain their brand names. For example, Hitler took over Renault in France and forced them to turn out military vehicles instead. Only an idiot would call this "right wing" as if it at all compared to the Republican party and it's modern platform. China, for example, disallows any other political party except the Communist party. At times they have allowed corporations to grow under their own brand names, and at other times, more recently, they've pulled the rug on that and re-asserted yet more totalitarian control. But we've never called China fascists. They've always been Communists, with relatively tigher or looser control of corporations, having initially started out with much more outright nationalization of industry by bureaus within the government (till they realized it leads more quickly to mass starvation) . Have the Chinese moved from left wing to right wing? No. They've been authoritarian totalitarians from the beginning.
In the U.S. today, it's the Democrats who most resemble an authoritarian dictatorship that seeks to extend that totalitarianism onto corporations, some of whom are glad to lend assistance, if the heads of those corps are partisan party members. Socialism? That's just a gimmick to pander for enough votes to seize power, and to distribute public funds in such a way as to maintain that power.
Will the new Italian prevailing party cancel every other party? Till then, they are blowing smoke whoever compares them to Mussolini's Socialism/Fascism (whatever you want to call his brand of totalitarianism).
Same for US politics. Until the Republicans find a way to cancel the Democratic party, it's insane to compare it to anything that came out of 20's, 30's and 40's Italy, Germany, Russia or China.
Today, it's the Democrats which are the home of cancel culture, and most obviously attack political opponents toward their goal of authoritarianism toward totalitarianism.