Every person benefits from a whole food diet, with or without Hashimoto's and hypothyroidism. Food is healing and can either cause symptoms to improve or worsen.
What do we know about Hashimoto's and hypothyroidism?
First, gluten mimics thyroid cells in the body. When you have Hashimoto's your body can attack gluten thinking it is your thyroid. This drives up your antibodies and causes your immune system to go into overdrive.
Second, with hypothyroidism by itself, gluten can still be a problem by causing nodule growth or goiters and also can affect T4 and T3 levels. There isn't a large amount of research on gluten and hypothyroidism, but there is enough evidence to support limiting gluten in your diet.
Third, dairy can mimic gluten in about 50% of people with Hashimoto's or in people with a gluten sensitivity. Also, many people are sensitive to dairy products. It is trial and error if you have a dairy issue. I advise to limit dairy products when you have Hashimoto's or hypothyroidism. I consume dairy in moderation, and I also choose A2 dairy when possible. This is a higher quality dairy.
Fourth, soy is known to affect thyroid function and especially can cause problems with thyroid medication abosrption. I recommend limiting soy products in your diet.
Fifth, nightshades and goitrogens can also be a problem. With appropriate iodine levels, goitrogens are not a big concern unless you have nodules or a goiter. Most people reacting negatively to goitrogens typically have an iodine deficiency. Nightshades are white potatoes, tomatoes, peppers and a few other fruits and vegetables. The key is to notate how you feel if eating these foods and eat them in moderation if you don't seem to have a reaction to them.
You want to eat a high protein, moderate fat diet with most carbs coming from vegetables and some fruits.