Let me get this straight. The shop requires staff that will taste and give honest appraisal of the food products they make. The food product they make contain meat, gluten, dairy etc. So is it not fair for them to preclude anyone who would not be able to taste/eat the food unless there was a valid medical reason. Humans are omnivores therefore unless there is a medical reason any limitation of diet is a lifestyle choice, and with all lifestyle choices come compromises. Once such compromise has to be that some jobs may not be for you.
I have nothing against vegetarians or vegans or meat eaters of whatever, personal choice is personal choice. I don’t particularly like caged hen produced eggs and don’t buy them, thus I wouldn’t choose to work at one of those places.