Just curious where your synonyms came from. The Webster's link didn't have them.
Here is the list from
Fascism Synonyms, Fascism Antonyms | Thesaurus.com
Nazism
absolutism
authoritarianism
autocracy
bureaucracy
despotism
racism
regimentation
totalitarianism
one-party system
party government
no where does it focus on Right wing, and again, I argue the lockstep democratic party that wants all control entrusted to the federal government(except when republican party policies are implemented) is far more filled with bureaucracy and regimented politically correct thinking and doing.