exceptions to your rule
Pretty much all of Africa except South Africa - highly homogenous, highly violent
ditto much of South America
Scotland is fairly white and we're still a violent bunch. Gun deaths of course way lower than the USA.
England less homogenous than Scotland, violent crime similar or less, gun deaths again low.
Most of Europe aint white anymore (as several people, yourself included have been pointing out over the years). No high gun crime either, less violent than UK or USA.
Russia - high gun crime and violence, everyone grey coloured.
I think your theory sinks.