Everything you described is a cause for RFID interference. Automatic-open doors at a grocery store, radio antennas, cell towers, etc. This is why you also cannot keep your cell phone in the same pocket as your key fob. There is no real solution to your problem, other than to find a different grocery store!

CAMRHEE Hybrid
Completed Mods: RK-Sport body kit, 18" LexusGS430 wheels 235/50ZR18 tires, TRD/SE springs, Rear Lip Spoiler, Terk XM-Direct, Smoked tail lights, Rear Bumper Applique, Front License Bracket, Lower Grill chrome inserts, K&N, Blaupunkt THB200A sub, moved rear HSD emblem
Future Mods: fog lights, black chrome my wheels