I definitely think there is no black & white here... it depends on the severity of the allergies.

I wouldn't breed a dog who was violently allergic to every meat source except venison, for instance. But, it's not a big deal if the dog gets an upset tummy when they eat lamb.

However, if I were breeding dogs, I would be hyper-critical about the health & conformation & worthiness of breeding my dogs; as any breeder should be! I think you have to honestly look at the dog's health as a whole.