I don't think I buy that. Take hockey for instance, a lot of the same build, strength, and stamina requirements of football but radically different demographics of players. The Black kid who dreams of making it and becoming a famous NFL or NBA player is a trope for a reason. They see people like them who made it and they pursue it like crazy, its no wonder they are over represented in certain sports. Or the fact that Black people live mostly in urban areas, where Basketball as a sport dominates, or the South, where high school football teams can have stadiums that make colleges blush.

I recall reading how ancient Greek cities would specialize in certain weapons. It might start that one guy from Rhodes becomes a famous bowman, so it comes that Greeks elsewhere expect Rhodians to be expert Bowmen and Rhodians themselves idolize their local hero and strive to be like him. Cultures often adopt and reinforce stereotypes in a positive way.