They probably do not have the Neanderthal gene because Neanderthals stayed away from them because they were racists! Cue the “That’s Racist!” kid.
So my question is this. Why is it that that Whitey has the gene and doesn’t act like one very often but the violent crime rate shows it is disproportionately in favor of those who do not have the gene but act like them?
Surely you’ve heard of berserkers run amok?
You are making some assumptions about Nenderthal behavior that are not supported. People just assume they acted like pure brutes because they were “cave men.” Actually early Homo Sapiens lived pretty much the same way. They made better tools, though.