You can use alternatives but you have to maintain them meticulously. If any of their websites or services can get a bit in, you're fucked.
Welcome to the world of quantum computers, pseudo-AGI and corporate interests.
Maintaining my own alternatives isn't a big deal. I'm largely doing that anyway.
Oh yeah, don't forget they are sharing this information with an ad agency who covered the installation cost of not only your grocery store, but also your bank and gas station. All of those prefernces, tied together in a neat little digital folder, ready to sell to the highest bidding government agency.
On your topic, I'm not totally helpless, though. I can't do anything about store surveillance except go to stores that don't do that (while they still exist).
That said... I can and so put my phone into airplane mode before I enter stores, and I avoid using credit cards in them, specifically to help protect against those kinds of spying.