My recommendation: Never, ever use the term “cancel culture.” Speak instead about the specific behavior you either want to reject or endorse.
OK, then. I reject progressive political orthodoxy. I reject the attempts to enforce progressive political orthodoxy by harnessing the power of social media to carry out organized campaigns of aggressive harassment, intimidation, and threats, usually directed at the target’s reputation, employment, or both. I reject the spirit of petty vindictiveness that motivates these crusaders. I reject the disingenuous arguments that “censorship” per se can only be carried out by a government, or that groups of fanatical activists preventing the willing exchange of goods and services is actually “the market” at work. I reject the insulting, legalistic, hair-splitting attempts by both cynical progressives and fatuous academics to simply define the entire phenomenon out of existence (see also, “critical race theory”). Most of all, I reject one of the oldest delusions in the history of this ridiculous species which steadfastly refuses to learn anything from its countless mistakes; namely, that the best of all worlds will come by giving in to our worst impulses.
Or, you know, you could just use a convenient shorthand term like “cancel culture” despite its unavoidable lack of precision and trust that those who aren’t being willfully obtuse will get your meaning.