What are the least worst non-perishable foods to have on hand... just in case?

Occasionally I'll hear someone say that it's not a bad idea to buy a few extra canned goods to have on hand considering how crazy the climate has been of late. I have a gluten allergy, lactose intolerance, and normally have to eat whole, non-processed foods in order to not have some kind of reaction.

Normally when I think of canned foods, I'll think of beans which I used to eat all the time, but now can only eat in small quantities before they start to upset my stomach. Same thing with grains and nut butters. So I'm not the ideal survivalist by any means. Has anyone with a bunch of food allergies and/or sensitivities found any viable non-perishables? Maybe I should just freeze some meat?