A goiter is an enlargement of the thyroid to counteract a reduction in hormone production. Goitrogens are substances that interfere with hormone production by suppressing the thyroid gland,  leading to a goiter. Many healthy plant foods contain goitrogens, including some fruits, grains, roots, seeds, and vegetables, but should eating them be  cause for concern for Hashimoto's sufferers?

Eating cruciferous vegetables like broccoli, cabbage, and cauliflower in their raw state may cause symptoms of hypothyroidism, as they contain glucosinolates  that block iodine uptake in the thyroid. However, don’t run from these healthy foods! Cooking or lightly steaming them will deactivate glucosinolates, as will fermentation (think kimchi or sauerkraut), and small amounts eaten raw shouldn’t aggravate autoimmune thyroid conditions.  Furthermore, most people with Hashimoto’s don’t have an iodine deficiency and shouldn’t be concerned about eating these nutritious vegetables.

The same goes for all other goitrogen-containing plants, with two notable exceptions : canola and soy. Besides being heavily processed, both are usually made with GMOs. Soy is particularly concerning for Hashimoto’s, as it has been linked to the development of autoimmune thyroiditis. Both canola and soy should be avoided.

Medications do affect sensitivity to goitrogens in cruciferous vegetables:  people on high dose thyroid medication don’t have to worry about eating them, but those on low doses  could be sensitive as their thyroid is still making some of its own hormones, and may feel cold if they eat too many. 

To sum it up: Hashimoto's patients need not pass on enjoying healthy, cruciferous veggies, especially when fermented, steamed, or cooked.

Sources:

https://thyroidpharmacist.com/articles/what-are-goitrogens-and-do-they-matter-with-hashimotos/