Most of our "mixed" ancestries in the West were mostly of similar European stock. There's a vast difference of a whole group of people with an ad mixture of Irish and Italians or Polish and German, than say someone who's half Scandinavian and half Bantu. Or the govt use of social engineering by transplanting people from totally different races and ethnicities and thrusting them upon a un-wanting populace.
You're either missing the mark or very good (in your mind) at creating strawmans Clare.
Either God intended people to be divided by language barriers (as per the Tower of Babel) or He did not, at least not in the long-term.
Now, if people are going to keep bringing up Babel to argue for separatism, they should argue against different nationalities mixing. They don't do that though (and the number of so-called "Nationalists" I am aware of who are married to foreigners is astounding!). So, really, Babel is neither here nor there.
It's tempting to accuse those who bring up Babel and Old Testament laws in the matter of race, of, ahem,
Judaising...