I've never worked at a brick & mortar retailer, so I can't know for sure. I know for sure that online retailers do this - a few have been caught showing different prices to different customers, or to the same customer in different browsers. I'd be very surprised if Walmart/Target/Safeway/CVS/etc. don't - what else is the point of the "rewards card" if not to gather detailed data? Why do they seemingly have a different "everyday low price" every month?
While I think you're right re:data (got my up vote for that!), Safeway club card is a bad example- 1) it's basket-wide and 2) almost everyone uses it. SW CC is good old fashioned price discrimination, which is designed to capture producer surplus from customers whose willingness to pay is greater than the market price. Many other examples incl. airline tickets: the extra charge for first or for a flexible ticket isn't because it costs that much to keep your spot flexible in their model, it's simply to price discriminate and be able to charge as high as the market will pay. Nothing wrong with it, but the key difference is that the sale itself does matter.