Okay, I misunderstood you, sorry.
Yes, the system as you are describing it makes no sense.
Fair Housing Act prohibits discrimination based on national origin
Maybe the USA is like this. I haven't and seen such an interpretation of "national origin" anywhere else in the world.
I have only ever heard the term "national origin" with respect to _citizens_. E.g. you were a Pakistani, married a Chinese took Chinese citizenship, you are a Chinese citizen, but your "national origin" is still Pakistani. Of course discrimination on the basis of something which is not in the documents is illegal. You are a Chinese no matter where you were born. But if you are born as Pakistani and are still a Pakistani, then the term "national origin" makes no sense.
Your proposed scenario seems like it breaks anti-discrimination law.
Again, possibly the USA is unique in this respect. Where I live (as well as my previous country) the anti discrimination law is strict, but it only extends to the government institutions. And I'm finding it baffling that it may happen to be otherwise in other countries.
State universities cannot reject students based on race or sex. Buses must carry everyone regardless. Police must accept complains from all. Of course.
But prohibiting private people from freely exercising their basic rights of liking and disliking whoever they want (and consequently making or not making commercial agreements with them) is such a mind-blowing example of tyranny that it's hard to even imagine for my third-world brain.