I have only heard of avoiding gluten, because the cells are so similar it could lead to celiac disease. I have 3 children with celiac disease, which makes me think that hashimoto's must be on one of those main celiac genes, also. My husband has hashimoto's---but I know there is no way I could convince him to eat gluten free. I have heard it suggested to avoid gluten----but i have never heard that it is a set rule.
I have hashimotos also. I have had it for 20 years. I have never had a dr tell me I had to avoid certain foods. Wish I could help. My antibodies were close to 4000.