No, you should keep enjoying them. It is true that cruciferous vegetables such as cabbage, kale, Brussels sprouts, broccoli and cauliflower contain natural chemicals called goitrogens (goiter producers) that can interfere with thyroid hormone synthesis. Other foods that contain these chemicals include corn, sweet potatoes, lima beans, turnips, peanuts, cassava (YUCA), canola oil and soybeans. Fortunately, the goitrogens in these foods are inactivated by cooking, even by light steaming, so there is no need to forego the valuable antioxidant and cancer- protective effects cruciferous vegetables afford.
However, if you habitually eat a lot of cruciferous vegetables raw, you should let your physician know. A simple blood test can reveal whether or not the dose of the thyroid hormone replacement drug you are taking is adequate. You should have a blood test once a year in any event. Your dose may need to be adjusted if you gain or lose weight, if you are pregnant, and, sometimes, if you start or stop birth control pills. Some medications, including antacids containing aluminum, can also interfere with thyroid hormone absorption and require an adjustment in dosage.
You should further be aware that excess consumption of soy can be a problem when you're taking thyroid replacement medication. Be sure to tell your physician how much soy you're eating so your dosage can be adjusted, if necessary. Eating soy foods at the same time that you take thyroid hormone can interfere with its absorption so, to be safe, don't eat soy within three hours of taking your medication. You are unlikely to run into a problem with moderate soy consumption - one serving a day of whole soy products, such as one cup of soy milk or one half cup of tofu, soy protein (tempeh), or crispy soy nuts.
Andrew Weil, M.D.