Race is real. U.S. race categories are not the same as used elsewhere in the world. U.S. Census categories map quite well to genetics. They capture a lot of variance. Ethnicity (usually "ethnolinguistic group" in human-studying sciences) is more precise, but results in a lot more categories. You can capture all the variance with infinite categories. This is the bias-variance tradeoff. This is how things are.
Even less so in the US with its weird categories that confuse the rest of us: I have never figured out how people with lighter skin then me (mixed white and south Asian) can be "black" or whether Spanish people are "hispanic".
It's not racist, because it doesn't say anything about the worth of the human or their rights. In fact, if you refuse to categorize and measure, because you consider this in itself to be evil, you can't actually cater to this specific person.
But I’m afraid that in practice, races aren’t biologically defined.