Of course not. Black people tend to have black hair. So do Asian people. The association is a simple observation of reality.
I understand statistical significance. The issue is that even in something like your birthdays experiment, we might find phantom "racial" differences. For example, let's stick with birthdays, but choose a date 9 months after Christmas.
In cultures that celebrate Christmas (mainly white), you might well expect a higher incidence of births as couples enjoyed "the Christmas spirit." But in other cultures, there's be no special correlation. Maybe you'd need to choose a different date. Are white people genetically pre-disposed to have children in late September? Nope. You just need to look beyond correlation to causation.
But the real problem, once again, is that you think that "race" is a real concept, that can be discerned, presumably, by similar looking skin.
As I wrote in the article, back when we didn't understand genetics, this wasn't an entirely unreasonable assumption. But in the year of our Lord 2022, having decoded the human genome decades ago, we know as a matter of fact that intra-"race" differences can be greater that inter-"race" differences.
You cannot look at two people with similarly coloured skin and assume they're genetically similar. Not in athletic ability, not in intelligence, not medically. This is a silly, antiquated idea that we should all know better than by now.