I know from direct experience in some parts of the South that the most common attitude, white or black, is that the Civil Rights struggle was so far in the past and so fuelled by extremists that it was best to put it behind them and move on. Unfortunately many extremists in the South and most extremists in the North were unwilling to let go to the point where race relations among typical Southerners now are objectively better than they ever were among Northerners.
Just my $0.02 from outside your country looking in.
I have become cynical, because there are so many "news" sources that will lie or misdirect to get you to believe things that aren't true.
Yes, i've heard that race relations in the South are better than the North, and what i've read over the years makes me think this is probably correct.
Most of the serious problems I hear about are in places like Chicago, Detroit, Washington DC and Philadelphia.
I've heard of troubles in Atlanta, Houston and New Orleans, but I don't think they compare to the stuff coming out of the Northern cities and Los Angeles.