I've come across conflicting info about iodine. Is it best not to supplement if you have hashimotos?
Iodine: I've come across conflicting info about... - Thyroid UK
Iodine
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think the short answer is don't supplement iodine if you have hashimotos
iodine deficiency can lead to an underactive thyroid so will help if the cause of the underactive thyroid is an iodine deficiency eg because there isn't much iodine in your diet - and it is difficult to guage how much iodine is in your diet. However too much iodine can can overstimulate the thyroid and cause problems - and if you have a thyroid condition that is causing your thyroid to be underactive supplementing is going to cause problems.
Most sources say no. But if you do decide to try it, you need the support of a practioner who knows about it and the thyroid, eg Roderick Lane in the UK - search web or try Thyroid Care Facebook group.