I used that label based on her writing. If you look at the positions she’s taken over the last half decade or so, they’re consistently on-message for what American conservatives are opposing: attacking #MeToo, railing against imaginary antifa (it’s been a while but that’s why she stopped writing NYT op-eds[1]), pushing COVID denialism, attack transgender people, and, most especially, being a committed member of the “cancel culture” marketing campaign. Whether that was hyping up IDW figures, defending a right-winger who is currently being criticized, or minimizing right-wing book banning or calls for people to be fired, she’ll be right there next to the rest of the crew.
Bear in mind that I’m not saying any of those are (or should be) illegal, only that on this topic she’s notably biased and quite literally makes a living from advancing this position. Her move out of journalism was based on building an audience with a pronounced bias and she’s not going to say anything which upsets them until she has another job lined up. Reading her blog posts on a culture war issue is like going to HuffPost expecting trenchant analysis of the Republican Party.
1. https://www.poynter.org/newsletters/2020/breaking-down-the-c...
That is really what it's about, not Bari Weiss.
As for your second paragraph, there is quite a lot of mischaracterization of what she has actually said and weird correlation equals activism claims. You haven't put forth anything that refutes the educated, competent journalist with views you disagree with counter hypothesis to your right wing activist claim.