That said, GP's point is that unless there are radioactive substances flying in the air / otherwise contaminating the store next door, things bought there should be safe. They'll be irradiated (affected by radiation), but not radioactive themselves. Contrary to popular opinion, getting irradiated doesn't cause you to become radioactive.
> getting irradiated doesn't cause you to become radioactive.
Well, actually... Neutron activation and photodisintegration via high energy gamma rays can produce radioactive isotopes via irradiation.
But this generally requires a high flux or high energy to produce noticeable secondary radioactivity. So depending on the type and energy spectrum of the radiation the sandwich is exposed to it might pick up tiny tiny amounts of radioactivity.
But yeah, that's probably going to be drowned out by any kind of radioactive dust.