You might be able to eat seaweed, were it pure seaweed, but there would be no way to be sure that the seaweed had not been contaminated by shellfish allergens. The iodine has nothing to do with the allergic reaction to fish and shellfish, so you are safe to eat iodized salt. Be aware, however that allergy to iodide is not rare, although unrelated to the seafood allergy.
Can an invidividual with a seafood/shellfish allergy that is known to have anaphylactic shock take a dietary supplement with Wakame™ seaweed 10% Fucoxanthin? Thanks for your response.