People care about race because race is about who your blood relatives are, and who, to some extent, your descendants will be.
A racial group can best be defined as an extended family that has more coherence and cohesiveness than a typical extended family because it is partly-inbred.
So, that’s why people care so much.
I think you are accepting the advertising hooey of martial arts dojos too much at face value. Most people don’t take martial arts for all the abstracted reasons that appear in the brochures, but because they want to feel they can win fights with other people.
Similarly, people don’t want to learn how to be rational for the sake of being rational. Instead, you have to sell rationality for more human ends, such as being able to win arguments, or make money, or understand a particular field such as baseball statistics. You can learn a lot of general lessons about rationality from reading Bill James on baseball statistics, but it’s not very exciting to study rationality for the sake of being rational.