Autoimmune diseases have the property that they like to co-occur with each other. If you suffer from Hashimoto's, which is an autoimmune thyroid disease, there is a good chance that you are also suffering from coeliac disease - another autoimmune disease, which affects the intestines rather than the thyroid. However, if you suffer from Hashimoto's, don't go on a gluten-free diet straight away. Get tested first and find out if celiac disease really affects you.