Food allergies can be non-IgE, like cow's milk, soy protein, eggs, corn, oranges, peanuts, beef, shellfish, refined sugars, alcohol, caffiene, and wheat. Celiac disease is also a manifestation of a non-IgE allergy.
Some examples of non-ige allergies:
Food protein-induced enteropathy, such as Coeliac disease, which is when a person has a big adverse immune response to gluten protein.
MSPI or Milk-Soy Protein Intolerance, which is an allergic response to soy protein and milk. This usually occurs in young children and infants. This allergy produces symptoms similar to food protein proctolitis (FPIES).