Why does this matter? Because most of the articles claims are based on "spoke to us" quotes from anonymous staffers which cannot be independently verified. So it falls to the reputation of those publishing and their journalistic integrity/process, and at that point I leave it to you to make up your own mind.
[0] https://en.wikipedia.org/wiki/Bari_Weiss#2017%E2%80%932020:_...
That doesn't sound like something she would say, and I've never encountered her making that claim. I'm pretty sure she got vaccinated and has encouraged other people to do so as well. She does seem skeptical of the ability of the vaccines to prevent infection by newer variants. To some degree, that's probably true right?