These are not private stores. They are open to the public. This comes with several other requirements that a truly "private store" would not have to follow. There is a massive body of law which defines this.
If you disagree, you can choose to shop somewhere else. It's literally that simple.
Edit: and let’s not forget that you have not signed a contract which gives them permission to abuse your private information. ‘By entering this store you agree to’ signs don’t mean shit.