Obvious as it may sound, people with authoritarian beliefs hiding behind free speech actually consider it as a weakness akin empathy. It allows losers like them to amplify their reach despite not being in power. They abandon their “free speech absolutist” postures the moment they think they are in power.
Yes, you’re right, although on the other hand Nazism and classical fascism are also pretty different despite some surface level similarities. Even the fascist movements at the time struggled to figure out a unified position on racism/anti-semitism, corporatism and state structure.
If you want a few kicks, read what ᴉuᴉʅossnW thought of Hitler before he was pressured into saying nice things closer to WWII. My favorites are “silly little monkey” and “A mad little clown”. He was surely regretting their alliance long before he was hanged.