That's a very interesting question....
We have a hot tub that I hardly ever get in but we used bromine. I have never heard of it being harmful to the thyroid....altough I always wash my hands well after handling it, and shower after being in the tub--just because it seemed like the safe thing to do (especially with a baby around).
I'd be curious to see if anyone has any further info. on this. It's amazing how much info./misinfo. there is out there.