The US RDA for iodine is 250 micrograms per day. Notice: MICROgrams, not MILLIgrams or mg. The RDA is based on preventing goiters, not on optimal health, so don't assume (ever) that the RDA is actually how much of anything you want to get. There's more to it than that. The Japanese RDA is 800 micrograms. The actual Japanese daily intake of iodine is more like 25-50 MILLIgrams per day, because they eat so much fish and seaweed. And the Japanese have lots less cancer than Americans.
It turns out that breast cancer is associated with low iodine levels, especially during a woman's teens and twenties. This is not about radiation, it's just about not getting enough of a nutrient that the breasts need. Breast cancer is terribly common. The thyroid uses the most iodine in the body, and here in the US there is an epidemic of hypothyroidism. It could be argued that we would be well served by taking in more iodine, like the Japanese do. And obviously we're not getting enough from our iodized salt. Some argue that we don't absorb iodine very well when it's mixed with salt.
The CDC and other sources are recommending that people who are exposed to radiation take 150 MILLIgrams of iodine a day. But 300 milligrams of iodine has the potential to suppress the thyroid gland, to shock it, if you will. And not all of us are directly exposed to radiation levels that high. So we probably don't need to take that much.
If you decide to supplement iodine, make sure you look at all your supplements and add up the amounts in each. There is iodine in my multi, and in my thyroid support supplement. The cheap and easy way to just get more iodine is the liquids in dropper bottles that you can find at the health food store. One drop is usually all you need for a day. You do not want to overdose!! There could be iodine in lots of supplements, so check!
Personally, I have been taking somewhere close to 1 milligram (mg) of iodine a day, and at that level, I think that my receptors are full of good iodine, and I am at a low risk of uptaking radioactive iodine. I'm paying attention to all the information that comes my way about it, and I will give you an update if there's anything that convinces me that for my own health, I want to take more or less.