That's a good thing. Our "non-whites" are the most successful minorities on the planet.
At one time, the eating, barbaric Germanic tribes were viewed by the Romans like you view "non-whites," as a degenerative people that are a threat to Roman culture. The unwashed German hordes eventually won out as the Roman Empire overextended itself and crumbled under its own weight, which likely set humanity back centuries (since the German tribes weren't the brightest bulbs in the bunch), but civilization recovered and now Germans are viewed (unjustifiably) as some kind of intellectually superior people.
My point is that civilizations evolve as they interact with more advanced civilizations. Your Germanic ancestors were flinging their own feces and hunting with sticks until the Romans showed them something called metallurgy.
Same thing is happening as the "non-whites" live in a more nourishing cultural and intellectual environment. Luckily we're not in ancient times anymore and don't have to "convert" them at the point of the sword. They can immigrate, go to college, etc. Sure, there's going to be growing pains and strife, but humanity will be better off in the long run.