There were multiple things happening in the same timeframe that were not all specifically related to the Civil Rights movement that had an impact though. You could have multiple outcomes depending on which movements actually occurred.
You could have the Civil Rights movement and then not had Women's Lib, the sexual revolution, and an increasing drug culture and you would get one outcome. Conversely, you could have had no Civil Rights movement but still had all of the others and ended with another outcome.
I think if the 60's never happened, that none of the societal upheavals occurred, that civil rights would have slowly been implemented over the past 50+ years and that, with a lack of some of that other stuff, it is possible that the black community could have ended in a better place. That being said, I think if the Civil Rights movement occurred and none of those other things were implemented, I could make the argument that things would be even better.
Studies across all races show that time and time again, the children of single mothers are more likely to live in poverty and grow up to commit crimes. In 1960 the marriage rate in the black community was 61% and in the white community it was 74%. By 2008 the rate in the black community had fallen to 32% and in the white community it fell to 56%. There are obviously other things at play outside of structural racism that are more problematic when seeking good outcomes for all. 2 parent households are shown time and again to be better for children to grow up in. So in a time when racism in this country was blatantly in your face and awful, some of that Leave it to Beaver attitude that we all shared anyway led to better outcomes in some instances IMO.
I know that people are going to read that and not be able to deal with what I actually said, so to be clear, I am not saying that it was better for blacks to be discriminated against. It was not. I am saying that when you look across all the variables, that while that one variable was obviously awful in the past, that many other variables (which are shown to impact quality of life regardless of race) were not nearly as bad. In fact, they were much better.
Everyone can have their opinion on what caused the change, but it is clear that something changed that decade and not all those changes were for the better (IMO).