Your skip level manager experience reminds me of an interaction with a diversity officer at my previous employer.
The company had hired a diversity officer and she began an initiative that requierd all company employees take an optional cultural course that was essentially something about power dynamics between culture/race. Since it wasn't really relevant to my role, I decided not to take the course as it was optional... until I found out it wasn't. I started receiving emails and phone calls from the diversity officer that I should take the course. I thought it was a bit weird and just ignored her. She then contacted my boss and told her to tell me to take the course. Starting to get pissed off, I asked my boss if the course was option, she said yes, then I said I'm not taking it.
I'm mixed race with mainly French and Indian ancestry and while I can pass for full white (albeit a white person that spends time in the sun), my skin is tanned just enough that I can pass for other ethnic groups as well. However, my name is undoubtedly French.
I then received an email from the diversity officer saying that I was an example of a problematic white person and that I was probably ignoring her because she was female and Indian. Then I was contacted by HR for discriminatory conduct and told to report to their office. When I showed up at the office, I could visibly see they were confused as they were clearly expecting someone that didn't look like me. Luckily for me, some of my family is Hindu and I happened to be wearing a religious bracelet I received as a present and I was basically able to fend off their accusations of racism and whatnot. Left the company shortly afterwards.