What is a recommended diet for someone with hypothyroidism, hypercortisolism, pernicious anemia, and a vitamin d2 deficiency?

Gluten free: Possibly gluten and dairy free. Malabsorption can be caused by gluten sensitivity damaging your gut cells. Test thyroid properly. Check free T3 and reverse t3. Ft3 should be in upper range and rt3 in lower range. If your ratio is off, you may need Armour Thyroid or t3, and synthroid (thyroxine) would be the wrong med for you.

Nutrient dense foods: Eat foods that are nutrient dense (like meat, fish, poultry, eggs, cheese, low starch vegatables and water) avoid foods that are not nutrient dense (like starches and sugars, including fruit) nutrient dense foods will increase your basal metabolic rate. On the other hand, starches and sugars impair thyroid metabolism via affects on your liver (which helps activate thyroid hormone).