If someone said "we have a right to food and housing," would you call them "batshit insane"? While I agree that we don't have a right "speak [our] minds and voice [our] opinions in public without fear of being shamed or shunned," you (and the author) are adopting a style of argument where certain positions are subjected to intense scrutiny. The first paragraph of the NYT op-ed doesn't stand up under that scrutiny but the rest of it does, more or less.
The blog just gets weird:
> It’s good that the Times is worried about speech-suppressing laws promoted by some conservatives, but it’s terrible that the Times is gullibly accepting the Right’s deeply dishonest assertion that it doesn’t engage in the sort of behavior it calls “cancel culture.” There is no serious argument that conservatives refrain from “cancel culture.”
Which part of the following quote from the op-ed claims that conservatives "refrain from cancel culture"?
> How has this happened? In large part, it’s because the political left and the right are caught in a destructive loop of condemnation and recrimination around cancel culture. Many on the left refuse to acknowledge that cancel culture exists at all, believing that those who complain about it are offering cover for bigots to peddle hate speech. Many on the right, for all their braying about cancel culture, have embraced an even more extreme version of censoriousness as a bulwark against a rapidly changing society, with laws that would ban books, stifle teachers and discourage open discussion in classrooms.
None of it! It says that conservatives have taken cancel culture further.
The author is worried that agreeing that cancel culture is a problem will help the right. But he does agree, so he does his agreeing in a roundabout way while heaping scorn on the op-ed. The overall effect is unpleasant.