"Being open to the public" doesn't mean they cannot use surveillance. They also have the right to ask you to leave, enforce clothing standards, etc. It's a private business - and a private building. They have a lot of rights about what happens within the premises.

If you disagree, you can choose to shop somewhere else. It's literally that simple.

Even if the law didn’t, humans have a basic right to privacy and anonymity from for-profit entities when completing life essential tasks. We’ve just become so cooked that it’s not even considered a problem for most, and not mandated by law to the extent that it should be.