The only information I have seen claiming that Hashi's is caused by leaky gut and gluten is all anecdotal. I have not seen a scientific study that confirmed that theory. One of the prime proponent seems to be a chiropractor who claims that the gluten molecule is almost identical to thyroid tissue and that is the reason for the antibodies produced against the gluten also attacking thyroid tissue. That theory doesn't explain why there are two different types of antibodies that are associated with Hashi's: Thyroid Peroxidase and Thyroglobulin antibodies. Even if a Hashi's hypothyroid patient goes gluten free whatever damage exists with the thyroid gland will remain and require replacement thyroid hormone med. I am also skeptical when I read about how the testing for this problem, along with treatment normally not available for them, was touted as a way for the chiros to increase profits in their practices.
So until there is scientific evidence proving the theory I am a skeptic.