Check out this site that lists some goitrogenic foods and chemicals (including other meds):
http://en.wikipedia.org/wiki/Goitrogen
Goitrogens are food that SUPPRESS thyroid function. So the foods that Gravegirl suggest, though appropriate for her since she is hypERthyroid, would be inappropriate for you with Hashi's. Please note that cooking destroys the goitrogens, so this is only an issue if these foods are eaten raw.
Many of us have not had to alter our diets at all to accomodate our Hashi's and meds. A good, well-balanced diet is all you need. Of course, if a particular food causes you distress, you should avoid it. It's usually only necessary to wait four hours after meds to take supplements. So, for example, calcium supplements should be taken four hours away from meds, but milk with calcium in it can be eaten half to one hour after meds, like any other food.
Milk is good for you...so, you shouldn't have to give it up unless you have a bad reaction to it. Processed foods are best avoided in any diet. Unfermented soy is indigestible. Soy is really cattle fodder, also best avoided by everyone.
I have Graves and all my research said to definately avoid dairy. I am on Methimazole for 2 months now and T4 has gone from 17 to 15 to 13 and now 6.2
Dairy has iodine that contributes to stimulating the thyroid. In hyper thyroid, that is the last thing you want to do.
Also eat tons of cabbage, cauliflower and brussel sprouts. I thought it helped me.
You can Google foods that affect absorption of Thyroid meds, Some are Cauliflower, cabbage, brussels, sprouts and brocolli, to name a few, Soy is out of the question, it not only affects absorption, but has a direct affect on the thyrois, In general, you should wait and hour after taking meds to eat, any minerals, vitamins, or Fiber you should wait four hours. I am not aware of Iron affecting thyroid meds when taken after the four hour period.
I have not heard of milk causing ant problems either, unless you have a parathyroid issue and have to watch your calcium and D intake, Good Luck FTB4