Food allergies are basically immune issues, and what I've read of them suggests that they're more likely to come from environment (the immune system gets antsy and starts attacking random harmless compounds when it doesn't have enough actual pathogens to shoot at) than genetics as such, so I think they're probably a non-starter here.

There's plenty of non-allergic variation in what different populations can handle food-wise, though; lactose intolerance and the alcohol flush reaction caused by differences in aldehyde dehydrogenase expression are the first two I can think of. These are often uncontroversially linked to ethnicity: lactose intolerance for example is very common outside North or Central European, North Indian, and certain African populations, and the alcohol flush reaction is a mainly East Asian phenomenon.