I've been a vegetarian for 14 years, but I've only known I was hypo for a little less than a year now. Before, I was forcing myself to eat those foods that are thought to be vegetarian substitutes, ie soy. I don't like soy, I think it is unnatural and disgusting so I'm glad that it is on the list of 'no nos'.
However, there are other vegetables and foods out there to eat. I still eat some of those vegetables but in small quantities and I try to eat them after several hours of taking my meds.
Not all of the goitrogenic foods affect my medication, some do more than others. For example, I might as well just cross broccoli off of my list because it is almost like I didn't even take my levo that day. But other things like strawberries don't seem to have any effect and it is ok for me to eat those.
Like Piglet has said it is a lot of trial and error. I've learned a lot of the past year as to what works for me and what does. For me white pasta is the enemy, I can eat great and workout all week but if I have regular pasta instead of whole wheat just one time, then I just trashed everything for the week.