Back in the first half of the 20th century, the rate of criminality in black communities was barely higher than the national average

Big difference is before Civil Rights black communities were self-policing. People that acted a fool got a whoopin' instead of a criminal record.

Murder rate in the '20s was about the same as in the '80s. Racial breakdown is hard to come by before 1960s, but if proportionally it was mostly whites murdering back then I'm sure we would hear about that all the time. White murder rate '60s+ is largely constant and the rate was already high before prohibition so there's no reason I can think of to believe the murders in the first half were by whites.

edit: to the point, murder rate is a good predictor of overall violent crime rate.