Every time I check out at a Kroger store I tell the cashier that I would like to get a membership card. They don't require you to give a phone number until you register the card after the checkout - which I don't do because I already got the benefit of the card at checkout. This won't work at stores that require phone number first, and still leaves open credit card-based tracking - for that you actually lose the few % cash back if you want to use cash instead.
I've been using the same un-registered Smith's (Kroger by another name) card for 5 years now. I get gas points and everything. Now, do they know a lot about me based on my credit card? Yes, but it's a start...
I have one of those too.. but only used cash with it. I have heard that if you use that and a CC or debit card they link the data - even if just once - and can link the past data as well.
I also have my wifi turned on my phone so they can't correlate the 'burner card' with that.. if I don't have cash I use a different discount card.
Of course if they scan the face and correlate that way - meh. For that reason I only use cash at Target - but not sure how long that will be enough to keep from data points being put together there or anywhere at this rate.
Every time I check out at Kroger (or similar membership-based store) I tell the cashier that I don't want a membership but I do want the listed sale price. They always just scan their own card.
CVS started to refuse to scan the 'house' card as of about a year ago. and they try to collect your phone number when they hand you a card for the first time.
