Everyone knows of Malcolm X and Black contemporaries of the Civil Rights Movement who did not believe that it went far enough in uplifting and liberating Black Americans. I've found little on if any prominent or even remotely notable Black voices stood in contrast to this, and were instead ENTIRELY resistant to the Civil Rights Movement's antiracist goals for one reason or another. I figure surely some noteworthy Black Americans were outspoken in their opposition to the movement's aims at the time, either due to their own conservatism, internalized racism, or because they were simply serving mouthpieces for White racists of the time. Are there any such examples?
I've read one excellent, thorough source that I cannot recommend strongly enough...but its answer to your question is rather indirect or at the edges of what she covered. Dr. Adelaide Cromwell's The Other Brahmins: Boston's Black upper class, 1750 to 1950 says many things, and it slightly makes the case against incomplete, poor integration that caused harm to Black professionals among others and was made without Black stakeholder involvement.
First, some background - Dr. Cromwell broke several color lines and is cousins with Edward Brooke who deserves several of his own books and /Askhistorians threads as a mid-century attorney general and Massachusetts senator. She got a sociology PhD in 1946 and was the first Black professor in a few mainstream, non-HBCU places before settling at Boston University where IIRC her family had lived for generations. This book is a reworking of her doctoral dissertation. It covers all sorts of aspects of Black life that can be measured with data she largely collected herself.
One profession that was somewhat, nominally integrated in Boston by 1950 and had enough Black participants to be analyzable post-WW2 was the medical profession. The general arrangement is you get a college medical degree, serve for a few years as an intern at a hospital, then you're a proper doctor and will either work in a hospital or doctor's office. In Boston, the hospitals had integrated for patients while in the Deep South, a Black patient who got advanced care at all would likely go to a colored hospital or the separate but equal (no!) colored ward of a hospital. Meanwhile, it was out of the question that White Boston hospital patients would be looked after by Black physicians. The consequence for a Boston college kid who plans on a medical career is that you attend college wherever - and elite Black kids were not unusual at mainstream nearby colleges by now. He then has to go to the Deep South for his internship, then moves back to Boston to open up a doctor's office and serve Black patients, employment at integrated hospitals not really being an option. Dr. Cromwell did not approve of this extra burden caused by this sort of partial, nominal integration.
There is an important story to be told by others what happened to the Black school principals and teachers who were removed or underemployed after integration to minimize White kids taught by Black teachers, also White women teachers working under a Black male principal. If anyone has info on this, please start typing!
EDIT a week later - The Lost Education of Horace Tate: Uncovering The Hidden Heroes Who Fought for Justice in Schools by Vanessa Siddle Walker also deserves attention. I've bought a used copy but not read it yet. The linked Atlantic Monthly review is very good. Consider a scenario where the local school district is willing to integrate, but at the same time, they will fire most/all of the Black teachers. The kids may end up in a school with a library and play ground and flushing toilets, but the White teachers will be something between apathetic and hostile to the interloping Black kids. They lose their old teacher who was overqualified with his master's degree and was an excellent role model.This piece of history appears to need much more attention.
most black conservatives are not against the advancement of race, they just disagree on the method to get there. we mostly subscribe to the Booker T Washington way — make money and work hard with the system you got instead of all the political activism that doesnt really get us anywhere financially (W.E.B DuBois). When you have money, racism is heavily diminished. People respect money more anyway, race is more negligible as you get to the top. They respect your money and accolades skill.