This is something a lot of people seem to believe that is not borne out in the research. Plenty of specific counter examples like Queens NY, a densely populated and exceptionally diverse place with crime rates comparable or better than many much more homogenous places in America. Poverty and income inequality are much better predictors. I felt this reddit comment from a while ago did a pretty good job rolling up sources on this: https://www.reddit.com/r/TrueUnpopularOpinion/comments/1jxff...