I could be wrong, but I've not heard of high fiber diet being bad for hypothyroid. I do know there are some foods, such as cabbage, broccoli, etc that inhibit the absorption of thyroid meds, but if you avoid those foods, you should be ok. I did a search for foods to avoid and came up with a list.
My doctor actually recommended the Mediterranean diet.
If I'm wrong, I'm sure some others will let us both know.