Absolutely, Karen. A shopkeeper may affirm that they reserve the right to refuse service to anyone, but they don’t actually have that legal right. Running a restaurant or a store in the US is what is known as offering a “public accommodation,” legally speaking. It’s generally against the law on the federal and state levels (depending on where you live) to discriminate against members of minorities in a public accommodation.
The details get quite complex in application, but that’s the general idea. So when that infamous baker in Colorado, for example, refused to sell a wedding cake to a same-sex couple, he was actually violating Colorado law. The Colorado Civil Rights Commission fined him and told him not to do it again.
He sued, and the Supreme Court decided in his favor on a technicality. Even though he won, the ruling doesn’t apply to other business owners. Other cases are pending, however, and conservative Christians are still trying to make a legal case for being allowed to disobey the various civil rights laws.
My arguments in this article are moral positions rather than legal ones, but lawyers who are well informed tell me we are at grave risk that the Supreme Court will allow religious exemptions to anti-discrimination laws, which would put even the venerable Civil Rights Act of 1964 at risk.