Yes they can and, unfortunately, even if you start paying by cash you’ll still be tracked to a certain extent. It is extremely difficult to avoid any kind of purchase tracking because everyone from the private company that manages the lot you park in before going inside, to the retailer, to your bank, to the smart screens in the store, to your fucking smart phone (whether by GPS or wifi network identification) is working together to identify and track you.
It’s really fucking hard to go incognito theae days.