So you seem to agree more with the "race is a social construct" people than it first appears since all the boundaries you talk about are fuzzy and arbitrary, you even suggest that people must be able to distinguish them with their own senses for them to be meaningful, and that if it's not a useful tool to humans then it's pointless. All of which sounds very social construct-ish to me.
Possibly you're just talking past each other, and don't fundamentally disagree at all.
When you take a big corpus of genomes and split them using impartial mathematics into similarity-clusters, you get clusters that almost perfectly match the continent-scale races that people self-report. That's not "arbitrary". Furthermore, people in these groups differ in characteristics that are measurable and important.
When I say that "race exists", I mean that there are real differences between the k={3,4,5} groupings and that almost always tell someone's group affinity by sight alone. The existence of marginal cases doesn't somehow invalidate the reality and utility of the high-level groups.
When people say "race doesn't exist", the general public reads that as "there are no differences on average between people from the various continents", and this claim is not only false, but it's so false that one doesn't need sophisticated instruments to tell.
I believe that this confusion is deliberate and is part of a misguided attempt to eliminate bigotry by delegitimizing the classification schemes upon which bigotry is built. This strategy is doomed, because you can't take away people's eyes and ears.
Possibly you're just talking past each other, and don't fundamentally disagree at all.