i don't remember the Tower of Babel appearing in the Quran or Hadith, it might appear in some tafsir because they basically just take Christian/Jewish tradition so its expected.
Quran and Hadith doesn't say anything about race unless you count the jinn; it speaks of nations and people groups, they're not really the same thing as race.
but if you apply anachronistically the concept of race, Muhammad says in his
Final Sermon:
But I'm not a muslim, so what do I think?
I don't deny differences of averages between population groups btw; that would be ridiculous.
the question is where does one race end and one race begin? there is something arbitrary about that, and the boundaries are drawn by outsiders.
race removes the gradient, putting a cutoff; if this was just a convenient classification that would be fine, but its treated as something more serious. race realists tend to treat races as units that follow their self-interest; this is only true in places where race is made into a social reality -- codified.
I did not grow up in a multi-racial country, but a multi-ethnic one, most people identify with an ethnic group and not a racial one. A race realist would say that the people of this country are the same race, but what do we have in common? well, its a gradient, more geographical proximity, more in common -- but what glues all these ethnic groups? a constructed national identity and not race.