To be fair, in medicine, drugs can have different effects on different racial groups. So differences do exist, just not normally in a person-to-person comparison. Race is a continuum.

Yes some genetic differences do exist. But the idea of race is still incorrect. There are
Regional differences. A 'Black' person from Northern Africa has important biological differences from a 'Black' person in southern Africa. Genetics are important but race is pretty much the first thing people notice about another person after gender. Then they make automatic assumptions about said person in regards to their race. Black, white, asian and Latino mean nothing in terms of shared culture, genetics, religion or even identity. That is why it is wrong. If we use the basic idea of race to treat people medically it would cause way to many problems as some people of a 'race' are not the same as others. Fortunately our doctors do not make assumptions on race often(well at least in terms of the actual treatment). Also what is deems Black and what is deemed Asian are wildly different. A person that looks black may not be black as we think of it. Same with Asian. The people of the Pacific Islands are quite different from those of Japan and the rest of Asia.