Yes, exactly. So saying "race cannot be meaningfully unambiguously described by a handful of totally discrete categories" is true. Saying it has no biological basis is clearly false, in the same sense that saying "color has no physical basis" is false, just because there is no clear way to exactly determine which pigments or wavelengths should fall into red, green, or blue (or how many and which primary colors there should be).
This feels a lot like the immigration debate in the US. One one hand it is actually sort of insane that undocumented people have all these rights and things as no other place on earth operates that way, but on the other hand the way the right side of the spectrum approaches enforcement and treatment of these people is so insane that it forces empathetic people to oppose them.
Race certainly has a biological element, but we empathetic people are forced into cognitive dissonance because the reason the right makes this argument is not because of science but because of racism. So, like immigration we are forced to defend a sort of insane position, claiming that race is something we've just invented, when there are very clear racial traits to be found in the human population.
Then our cognitive dissonance is weaponized against us to argue that our aims are irrational.
