Trade law in Europe works like exactly that: you do not get to choose your clients; you either have to serve anyone that is willing to pay, or no one at all. The US should definitely adopt this principle.
It does, in some ways? Your business can't discriminate based on protected characteristics, like race.
Many customers aren't wanted, even if they happen to have money to spend.
I don't even like this. Shoplifters should all go to prison, but once they've paid their debt to society and been rehabilitated, they should be allowed to do everything that law-abiding citizens can do, including going back as a legitimate customer to stores that they previously stole from.