Mussolini and Hitler thought their projects were incompatible with communism/socialism, it's why their first steps upon achieving power in their countries were to purge the left and ensure that left resistance couldn't be organized against them

I think something liberals trip on is that Hitler and Mussolini didn't just attempt to suppress leftists. They did that after gaining power. Before gaining power they did any number of weasel-like things to convince the average person that fascists were in fact better socialists than the socialists. They appealed hard to working class interests, especially the ones with national chauvinist tendencies. They appealed to racism and scorned international cooperation. It didn't help that the average person in this was often confused, coming out of the problems of post WW1 Europe, and mainly wanted a party that would put food on the table. The so called "beefsteak nazi" was a type of person who'd join the Nazis believing they'd put forward more genuine socialist policies. Beefsteak, red on the inside, brown on the outside. Then you had people like Ernst Röhm and Strasser, who identified publicly as socialist. Then once gaining power in 1934, they were killed.

Fascists don't really have beliefs so much as they're an emergency tool for capital to rid itself of its primary internal enemies.