When people say a person of color sounds white, they mean that person sounds middle-class. No black person tries to speak like working-class whites from, say, Appalachia or Brooklyn. It shows how race and class are conflated in the US because rich people hate talking about our class system.

Incidentally, black women now do better than their white peers, though black men do not: https://comrademorlock.medium.com/why-black-women-are-now-privileged-but-black-men-are-still-penalized-6d208626a5c3