The State has the power, under the Constitution, to regulate such things as it and the citizens who elect it see fit.
If the residents of a State want to pass a law that you cannot rent to someone without them providing proof of legal residence that is not an abrogation of private property nor against the Constitution.
States ban and regulate private commerce all the time. Try selling raw milk. Try opening a business without a license. Try to put up a sign on your business saying “no ________ allowed”.
Try reading the 10th Amendment again and then come back and tell me that the States have no such power under the Constitution.
I’ve done all of those things. I have bought raw milk and drank it. I’m a farmboy and we do all kinds of things that would make the government keel over if they knew about them all. I’ve operated a business without a license and done quite well for myself. Kept myself busy and paid all my bills.
I’ve rented numerous places from friends and family and other folks without ever getting the goobment involved. That to me is real freedom.
As a business owner and operator, I don’t have to solicit or accept any business that I do not want. There are plenty of folks that I will not work with for the simple reason that they have been poor patrons. I’m allowed to make those eminently business decisions, because that is what it takes to keep operating.