My advice: plug your ears with an iPod.
Although I have had to overcome my initial fear of looking like a rich white consumermensch, I routinely wear my iPod on those large family grocery shops. I do, even in summer, figure out how to run the wires in as inconspicuous a way as possible. But here's my reasoning: supermarket chains feel they have the right to routinely and continuously bombard you with musical crap that marketing research has demonstrated will calm down fretful consumers. This is just the kind of musical dreck that is designed to stick in my head, where it completes its initial assault by morphing into a repetitious sonic brain cancer.
So I run my own radio show. I pause the feed whenever I have to talk to someone (e.g., at the meat counter, or while checking out) because I think it is rude not to knock them my lobes, as Lord Buckley says. But otherwise, I'm marching to the beat of my own damn soundtrack.
Sounds like a small thing, but: I bet I can remember at least 30 jingles from the TV ads of my youth ("its Kenner, its FUN---AWK"). They are permanently wired into my brain and I can't reuse the storage.
It reminds me of a scene from some Dustin Hoffman film, I don't know which one, where he's riding in an elevator and winds up into a huge rant about the elevator muzak: "WHO'S RESPONSIBLE FOR THIS?" he screams. I feel just as (perhaps eccentrically) enraged by commercial sonic assault.
Have a jingle-free day.