It's an additive to a lot (a LOT) of foods.
So you should avoid all non-traditional Asian soy foods if you're hyperthyroidal.
That's far more difficult that it seems.
"Whether you know it or not, you'll probably be eating soya today. It's in 60% of all processed food, from cheese to ice cream, baby formula to biscuits.
"'We discovered quite quickly, ... that soya contains toxins and plant oestrogens powerful enough to disrupt women's menstrual cycles in experiments. It also appeared damaging to the thyroid.'
"More than 60% of all processed food in Britain today contains soya in some form, according to food industry estimates. It is in breakfast cereals, cereal bars and biscuits, cheeses, cakes, dairy desserts, gravies, noodles, pastries, soups, sausage casings, sauces and sandwich spreads. Soya, crushed, separated and refined into its different parts, can appear on food labels as soya flour, hydrolysed vegetable protein, soy protein isolate, protein concentrate, textured vegetable protein, vegetable oil (simple, fully, or partially hydrogenated), plant sterols, or the emulsifier lecithin. Its many guises hint at its value to manufacturers.
"Soya increases the protein content of processed meat products. It replaces them altogether in vegetarian foods. It stops industrial breads shrinking. It makes cakes hold on to their water. It helps manufacturers mix water into oil. Hydrogenated, its oil is used to deep-fry fast food."
It doesn't help to go for all-organic foods, either: the organic crowd embraced soy protein lo-o-ong before mainstream production did.
Read labels religiously, and ditch all and any "vegetable protein", "protein concentrate", "plant sterols", and of course, anything which even remotely resembling the three letters s, o and y, and your thyroid should be safe. Or at least, safer. (I don't know how bad lecithin would be, sorry.)
Soy oil is another problem (from the same Guardian article):
"Soya oil - high in omega 6 fatty acids and 18% of the whole bean - has meanwhile driven the postwar explosion in snack foods around the world. Crisps, confectionery, deep-fried take-aways, ready meals, ice-creams, mayonnaise and margarines all make liberal use of it. Its widespread presence is one of the reasons our balance of omega 3 to omega 6 essential fatty acids is so out of kilter."
And soy sauce isn't a real old-fashioned Asian food anymore:
"In so-called "naturally brewed" soya sauces the processed soy protein meal is mixed with the mould spores and given accelerated ageing at high temperatures for three to six months. Non-brewed soya sauce, the cheapest grade, is made in just two days."
(Used to be, you'd boil the whole beans for three days and then let them ferment with their mold spores in salt water for 18 months. Not anymore, they don't.)
I expect that the production process of miso is as shortened as that of soy sauce, these days.
So. Tofu shouldn't be problematic - if it's ingested in small doses, not as the main course. I have no idea about tempeh, as I've never seen it, and even less eaten it.
Go read the whole grauniad article on soy foods, it's fascinating reading. And good luck in pursuing your diet free of modern-day soy foods!