Authoritarianism isn't the same as fascism. But the good guys don't side with the dictators and definitely not with the side hurting others even if they think giving in means the pain would stop.
Trivializing the Holocaust means to let bullies keep going unopposed and those that would trap and use others for labor or eradication which obviously can come from both sides but doesn't mean you pretend the easiest answer is right.
Right answers are hard and are likely at the end of hard work and effort, constantly. So maybe stop hiding behind a simple answer and a single fact that makes you feel you have a rule we are all breaking and realize it's gonna take a long and complicated answer and then come back and join the conversation.
We are not equating "communists" with fascism, we are equating authoritarian communists with fascism. They are both as bad because they are both authoritarian regimes that are based around opressing the people.
And holicaust trivialization? Didn't the URSS kill a shit ton of people as well? Isn't China commiting crimes against humanity as well?
If you think the USSR is an "authoritarian"(whatever that means) communist country and you are equating it to fascists you are doing what the Jewish holocaust scholar is calling holocaust trivialization. They are primarily talking about equating the USSR and fascism. Did you read the article?