Be cautious of: Gluten
We say that because this applies to people who have gluten intolerance and celiac disease. You already know that living with these ailments means that you should make sure that you eliminate gluten from your diet. This is because most of these types of gluten intolerances and thyroid diseases have an autoimmune origin and frequently coexist. So there is a chance that there may be a connection between the two.
This does not mean that having a gluten-free diet is going to help treat any thyroid diseases. However, if you have also been diagnosed with celiac disease, it is important to avoid gluten at all costs so that you can keep the symptoms at bay and eventually prevent any thyroid damage.