First, I think you're lumping "the left" together and assuming "the left" believes whatever the most extreme "left" tweets say.
Second, Bari Weiss can write whatever she wants. Totally her right. She's got a website there in the link! She can continue to reach a global audience. Does the NYTimes need to promote her? No, that's not a right I'm willing to die for.
Third, why on earth is Bari Weiss' opinion more sacrosanct than mine? If she says something I consider offensive, I might say I think it's offensive. If she says something dumb, I might say I think it's dumb. If she says something astute, I might say I think it's astute. She has a HUGE megaphone, so of course lots of people will respond to her. That's not "cancel culture." That's a side effect of having a huge megaphone. With great power comes great responsibility, etc.
Fourth, when I hear people complain about "going against the progressive party line" or whatever, I generally hear people wanting to be some flavor of racist, sexist, transphobic, or just asshole-ish without consequence. Oftentimes people in marginalized group react in a way that feels extra venomous to those of us not in those groups because they can feel their lives are constantly hindered and harmed by the sorts of thoughts that other people can just toss out and then walk away from. If this happens, I might suggest listening to the free speech from those people and trying to understand rather than writing screeds against "cancel culture" or whining about how you, as a very well-publicized and probably quite wealthy writer having your rights squashed. And that's why the Harper's Letter was annoying.