Well, race has no basis in biology and gender does, but I get where he's coming from. You can tell a male skeleton from a female skeleton almost instantaneously but it takes all kinds of tests and stuff to determine the race.
Race has basis in biology too, lol. The fact that you can determine a person's ethnic background based on their DNA and skeletal structure is proof of that.
Ethnicity is real, grouping those ethnicities into 3 (or 4 or 5 or more) "races" is not.
Anthropologists classify ethnic groups into larger categories all the time (but I get what you're saying).
Indeed, this is literally what is done to classify species.
All of these things have a base in biology but they are still subjective to a point. With sex, it’s a discrete value but there are rare exceptions and there could be a molecular sex and sex as defined at a functional level. Just because you have a Y chromosome doesn’t mean you can get someone pregnant but you can’t say that there’s more than two sexes.