I am an white, male, middle-class, professor of sociology. I may be biased because of my race, but my profession is to study and teach social consequences and social movements.
The most lasting influence of the Civil Rights Movement is the idea that black americans and black american culture should never be reconciled with American culture at large. For a black person to act white is an insult to their ancestry and a betrayal of their black brethren - this was said both by Dr. King and Malcolm X.
Think about what you learned during your history classes - how many white civil rights activists can you name? How many black confederate soldiers can you name? Who sold blacks into slavery in Africa? How many white slaves can you name? The way we teach american history emphasizes the conflict between races rather than the cooperation of races or the conflict within races.