Wanting to exterminate ideas is definitely not a fascist tendency.
I really cannot wait for the pendulum to swing back the other way. I am going to be absolutely insufferable about it until I die. These people have gone so far over the line.
I'd say eliminating patriarchy or fascism is coercive, but not (necessarily) authoritarian and definitely not fascist:
Coercive because you're using force to suppress the idea (e.g. punching Nazis, canceling abusers.)
Anti-authoritarian if the people are organically self-organizing to punch Nazis. More authoritarian if a centralized power is drafting people to punch Nazis.
Not fascist because fascism is inherently far-right, and predicated on enforcing a "natural" power hierarchy.
The Paradox of Tolerance justifies the forceful suppression of fascism and patriarchy. But imo you have to be careful - I limit my application of the Paradox of Tolerance to ideas that intrinsically cannot coexist with freedom of thought.