The junk data will follow us around and potentially be more damaging in the long run. The cashier used to have a card she would use to give the discounts if the customer didn't have a personal card. Now they aren't doing that anymore. We raised such a stink here that the stores kind of have to accommodate or they look bad. Also, they are reluctant to void out all of the card-priced items when you refuse to pay the higher price.
Some stores are less flexible than others.
I suggest you send a letter to your Attorney General, and also to the papers. My letter to the editor of a local paper led to a call from a like-minded soul and together we did make an impact, as the web site will attest. The stores want to know what we buy so they can provide those products. Here in New Mexico Furrs Supermarkets, a longstanding local corporation and the first to go to a shopper card program, has recently gone bankrupt. Many specials now require you to use a coupon and the card, and they require purchase of multiple items to get the lower price.