The words "Fascism" and "nazism," and "socialism" and "communism" "marxism", "leninism" and "capitalism" were around before we thought in term of left/right thinking. Its an example of gross simplicity fallacy.
We need to get back to definition of terms. Leave right/left behind and let's talk philosophy. Most of the "isms" are just a rebranding of older ideas mean to enslave us. With the exception of Individualism. Individual freedom is antithetical to both the current right, and left.