When I was in college in the late 1990s and early 2000s, people from the rural South were at times told they should lose the Southern accent because it would hurt their ability to get hired in jobs like finance and engineering especially in the Northeast. This was at a college in the Midwest.
If you go to New York, Boston, or Silicon Valley and try to break into a top-tier industry with a thick Southern accent and talk about how much you love to go deer hunting, this will absolutely put you at a disadvantage. I lived in Boston for five years and one thing I learned is that even being from a poor or "flyover" area of the country makes you a lower class of person. There's a very strong but quiet classism, especially in the Northeast, and the Northeast is the cultural heartland of American liberals. "Where did you go to school" is the biggest class marker, followed by where you're from.
Is it as big of a disadvantage as other things? Probably not, but "the oppression olympics" isn't a good take or a good strategy.
BTW -- every human culture has class markers and in-group out-group dynamics. It just seems like the US left is blind to the fact that they have these too, and no it's not all about rejecting Nazis and misogynists. Everyone from the rural South or Midwest is not a Nazi or a misogynist. Most are not.