Food allergies predate vaccines by millennia with Hippocrates of ancient Greek being the first to document food as a cause of illness and potentially death in the historical record. The exact cause of the INCREASE in peanut allergy prevalence is undetermined from what I can see, but some suspect vaccines, but given we're discussing the human body's potential to make mistakes, that would at worst prove we can exacerbate it, not prove the allergies are exclusive due to them. https://www.sciencedirect.com/science/article/pii/S1323893016301137