TugboatEng…
The Axis Fascists were actually Socialists, so left-wing not right-wing (I don't enough about Franco's version of Fascism to comment there). Benito Mussolini, the original Fascist leader, was an avowed Socialist and he ended up nationalizing something like 2/3 of the Italian economy. Alfred Rosenberg, the chief Nazi ideologue, was also an avowed Socialist and the Nazi Party advanced a mostly Socialist agenda. Adolf Hitler, though, took a somewhat less doctrinally "pure" approach to Socialism than did Mussolini. Hitler hated capitalists and capitalism just as much as he hated communists and communism. But, he made a deal with the key industrial leaders because he needed their support. The industrial leaders made a deal with Hitler to preserve their special position in the economy and because they thought they could control him. Hitler came out best in that deal, just like he did with the Army high command.
In the end, the Fascists had far more in common with the Communists than with the Capitalists. As for the Fascist's hatred of Communism, I have never seen a good explanation of it, but my own supposition is that Fascism was intensely nationalistic and the Fascist leaders probably felt threatened by Communism's internationalism. Well, perhaps also they didn't want any competition on the Dark Side of the Force.
Fred
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"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill