The civil rights movement was about ending poverty for everyone, which would disproportionately help people of color. The Dream Speech was delivered at the March for Jobs and Freedom. King wrote about his support for Guaranteed Income. He was planning a Poor People's Campaign with people of all races when he was killed.
The Ivy League exists to keep the US divided between the rich and the working class. Harvard is quite racially diverse today, but that has done nothing to slow the growth of the wealth gap between the rich and the rest of us.
The black working class is very aware that the black bourgeoisie has abandoned them. This is from 2007: https://www.pewresearch.org/social-trends/2007/11/13/blacks-see-growing-values-gap-between-poor-and-middle-class/