Naw, it’s real…it’s not like your genes form a little homonculus that rubs out foreigners. (If that was the case, successful mutations wouldn’t survive past one generation.) Here’s a couple articles on Neanderthal/Denisovan contributions to modern human DNA*:
One
Two
Heck, we still have proto-fish DNA in us (like Noggin and BMP-4 that give our developing embryos a top/bottom orientation). Or, from even earlier organisms, the genes that direct invagination (the self-construction of tubes – like Ted Stevens’ internet, our bodies are primarily a series of tubes; -) Maybe check out Neil Shubin’s Your Inner Fish for a layman’s primer on the depth of our genetic inheritance.
*except “true” Africans, whose ancestors didn’t migrate up into Eurasia and then beyond in time to interbreed with Neanderthals or Denisovans before they became extinct.