I think we split based on gender and race because those are clear discriminators. Height or hairstyle are more fuzzy, and probably biologically less relevants to adapt to the environment.
When I said clear discriminator I mean they are binary: either make or female, either black or white. Height or attractiveness are more diffuse for some people you can be tall/attractive but not for others. Gender and race are clear.
In my opinion height or attractiveness play a role in the society (a big role), but it is easier to talk about gender or race because the clear distinction, bigger represented groups and historical reasons.
I am sure I could find a study showing that attractive people have a better shot at getting the job. Height is attractive.