Cursory Google search seems to indicate that some fruits, as well as potatoes (!), dairy products, fish, and eggs contain iodine. Even if you were a very poor European peasant in the middle ages, you would still get to eat potatoes, milk, and smelly not-fresh fish, so the iodine problem probably would be bad but not terrible. If you were a rich person or someone who lived on the coast, I would speculate that you'd be pretty much fine.
> Even if you were a very poor European peasant in the middle ages, you would still get to eat potatoes
No, you wouldn't, as a European of any social class, except maybe in the very late middle ages at the boundary of the Renaissance; potatoes were a New World import in the 16th century, which might just still be considered the Middle Ages in some parts of Europe.
Preserved fish (dried, smoked, salted, or pickled) has been a common food for millennia. It's arguable if it's "smelly", it's by definition not fresh, but it's definitely fine to eat.
It was an important source of protein in centuries past, and was traded all over Europe. It would've also been an effective way for inland residents to get iodine.
As I understand it, the iodine in dairy typically comes from the products used to clean and sanitise the milking and storage equipment (iodophor). It's not inherent in the dairy itself, otherwise we could just eat the cow's grass to obtain iodine
The Catholic church has a rule not to eat meat on Friday and fish was popular instead. Not sure when that started but maybe forcing a bit of more expensive fish into the diet was quite useful for dietary health.
Before refrigeration and the steam engine fish prices would rise dramatically and quality decrease quickly as you move away from the ocean. Salting was done to preserve some types of fish, but this processing would add cost. As discussed elsewhere, people inland are the ones who would lack iodine in their diets and in those locations and I would guess fish would be the more expensive than meat in those locations. It would be interesting though to see a list of market prices for meat and fish from some inland city back then.
