Jessica, I think the problem with this:

"There’s been some backlash claiming the idea of “Karens” is a sexist trope, that singling out white women’s behavior is unfair. But the way these women are weaponizing their privilege is important"

Is that it is insufficiently differentiated. While the women who's behavior is unacceptable are white they are not the majority of white women. Using racist and sexist labels is problematic. Find a label that is more differentiable. Maybe something like self-centered, privileged, upper middle class snob Pats

TEK