I have NEVER, EVER given up my bags when I went into a store. I routinely carry a backpack into Walmart, King Soopers (owned by Krogers), Safeway, Albertsons, Ace Hardware .... I actually take my WHOLE bike with panniers and all into Lowes and Home Depot (Grocery panniers make GREAT shopping carts!). I've never gotten more than a strange look at any of them.

Hell... I even take my bike into the bank with me. (This is their main branch... marble floors, counters, etc.) ... Never get a second look, and get lots of comments about riding my bike.

I can only remember one time that I was asked to give up my backpack and I told them something not very nice that they could do to themselves and took my business elsewhere.