I take Armour Thyroid 60 mg. a day & have been oil pulling for a week now, usually 3 times a day, varying the types of oils as I experiment. So far there have not been any negative effects at all. If anything I may actually be feeling stronger - but there are different things I have been trying so it is hard to say what is doing what all the time.
P.S. If you haven't seen the website stopthethyroidmadness.com, you might like it. Check out what it says about the adrenals & adrenal testing too. It led me to find a doctor who did urine testing for adrenals & that made a major, maybe eventually life saving, change in my life thru adrenal meds.