Sometimes memes like this hardly qualify as a joke and it's very difficult to explain...but here's my attempt:
People on the internet like to complain about everything, so in this case, I believe the purpose of the meme is to diminish or disrespect people who have or claim to have a nut allergy. Some people either don't believe people have nut allergies or they just think that the sudden, dramatic rise in nut allergies (or the people who have/claim to have them) is a sign of societal weakness.