If literally true as you have written it up, it's pretty stupid; e.g. a brick-and-mortar store should be able to ban someone who shoplifts, or harasses staff or customers.

> a brick-and-mortar store should be able to ban someone who shoplifts

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.

law-abiding citizens can get banned from WalMart too

> The US should definitely adopt this principle.

It does, in some ways? Your business can't discriminate based on protected characteristics, like race.

Are there any limits to that principle? What if a particular customer openly advocates for, let's say, the destruction of the state of Israel? Should a business be required to serve that customer?

On the contrary, plenty of business in European countries have "We reserve the right of admission" shown quite visible.

Many customers aren't wanted, even if they happen to have money to spend.

In "Europe" (i.e. the continental protectionist bloc), even ISIS has the right to service.