IgE Allergy to cereals is generally rare; prevalence of cereal-related diseases are highest for wheat and lowest for oats.
All varieties of oats contain gluten and avenin, which is a prolamin similar to wheat gliadin which can be the cause of allergic reactions.
An allergy to wheat has been sometimes been linked to Exercise Induced Anaphylaxis due to the prolamin proteins.
Coeliac disease is not an allergic condition, but is triggered by gluten found in wheat and there are similarly shaped proteins in lesser quantities in oats to which sensitive individuals may react.
Oats are in the Poales order of foods, so there may be some cross reactivity with other foods in the group such as wheat, barley, rye and maize.