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There is no constitutional law against discrimination based on nationality.

What about the Fair Housing Act?

"The prohibitions specifically cover discrimination because of race, color, national origin, religion, sex, disability and the presence of children."

National origin is not the same as nationality. There are countless rights that citizens have that non-citizens do not.

National origin and nationality are different things.

Why? You have to have some legal residency to get a driver's license. Why not to buy a house?

Not if it was equally applied to all nationalities.