If you want anonymity, by all means, use cash and leave your Kroger Plus card at home. If you don't think they can profile and track you already by using your credit card / ATM card / 'Kroger Plus' card, you're fooling yourself. Plus, with the facial recognition software they have potentially scanning all the CCTV cameras in the store, you can be 'scanned' that way too. At least the fingerprint thing is voluntary as long as you use cash or an ATM/Credit card, and your fingerprint can't be stolen (at least not without you missing it!).
I know a lot of you guys are paranoid, and as they say, even paranoid people have enemies. I guess my point is, I don't know what my point is! I would probably use the fingerprint thing, becasue I'm a technophile / geek, and since I already use my Kroger Plus card even when paying cash, those Kroger JBTs already know that I drink too much Coke, eat too many chicken wings, and buy 'American Handgunner' every two months!