A March 2017 study by the American College of Allergy, Asthma and Immunology concluded that,
“among people allergic to one nut who have a positive test to other tree nuts, more than half passed an oral food challenge to other tree nuts without a reaction. Passing an oral food challenge means you aren't allergic to that nut. Tree nuts include almonds, cashews, walnuts and hazelnuts, but not peanuts.”
The study also noted that “nearly none of the people allergic to peanut, but sensitized to tree nut, were clinically allergic to tree nut. This is the first study indicating that peanut allergic people may not need to avoid all nuts.”