Is writing "white, female, upper-class" as bad as I think it is?

No, but that’s just because everyone wants to refer to themselves as “middle class” or at most “upper middle class”

Unless she wasn’t supposed to mention SES in that section, I don’t see the issue - unless you think she’s delusional about your family’s wealth (which odds are, she has a better grasp than you do).

Better to be privileged and acknowledge that one is privileged than to be privileged and try to pretend that one isn’t.