There is only a small amount of research that discusses the potential of kale causing hypothyroidism. Kale and other vegetables are a type of goitrogenic vegetables that includes arugula, bok choy, broccoli, brussel sprouts, cabbage, cauliflower, collard greens, mustard greens, turnips, and watercress.
Goitrogenic vegetables have an ability to interfere with iodine absorption that can lead to the swollen neck that we call goiters. To ensure that can relieve the goiters, aim to increase iodine intake to at least 150mcg per day. They are in your daily table salt.