It's pretty obvious that the reason the NYT is doing this is that someone was fired who they saw as being on the same side as them, for online speech they were extremely sympathetic towards, due to stuff dug up by Republican supporters. This particular issue is heavily tied to the US political divide: supporting Palestine is seen as a left-wing thing, and labelling those people as anti-Semites a right-wing tactic.
Which, I think, probably says something about how likely it is that people genuinely believe the talking point invoked in this article that the right-wing is the real cancel culture. If it was, it wouldn't be so shocking that and news-worthy that it happened, and the sole other example in the article wouldn't be someone from 2004 who built a career in media thanks to the supposed cancellation - exactly the kind of thing the press would point to as proof "cancel culture" isn't real if the left were the ones calling for her head.