Coconut Oil Hydrogenated : Whether coconut should be considered a tree nut is a matter of some controversy. The FDA mandates that coconut be considered a tree nut for labeling purposes; however, as the Food Allergy and Anaphylaxis Network notes, coconut allergies are exceedingly rare, with fewer than 10 reported cases. A June 2007 study in the Annals of Allergy, Asthma, and Immunology indicated cross-reactivity between coconuts, walnuts, and hazelnuts in one patient. Your allergist can advise you on the suitability of coconut for your diet.