I don't see the problem with identifying people to be members of a certain race. The DNA similarities are irrelevant. If our brains naturally divide people into categories based on shared phenotypes, then why try to deny it?

I don't see what the problem is with identifying black people, Hispanic people, etc. and putting those labels on them. I can only imagine it would be a problem to people who fear racism and are perhaps subconsciously racist themselves, and think there is anything wrong with being in a certain category.

You might as well say that no one really has a hair colour and that judging someone to be a 'blonde' or 'brunette' is a social construct.