Our WalMart does have a bike rack - located far away from the front door and traffic where everything could be easily stolen. I have never had to take my bike into WM, and don't know what their reaction might be - but I would suspect in this heavily biked town that it would be fine.

My local grocery also has a bike rack located way far away - I and my wife just ride our bikes inside the "air gap" type of front door and place our bikes against the wall inside - never had any questions asked.