There is currently no established evidence that GLP-1 receptor agonists directly treat or improve Hashimoto's disease or its underlying autoimmune pathology
Monteith AJ, Miller JM, Maxwell CN, Chazin WJ, Skaar EP
North Bethesda, MD: The United States Pharmacopeia (2016)
The article says the decision belongs with the endocrinologist or primary care provider who knows the person's full immune and thyroid history, and that a candidate needs a separate clinical indication such as obesity, type 2 diabetes or cardiovascular risk plus stable thyroid disease on levothyroxine
10.1161/ATVBAHA.107.160713 104 LuengoA.GuiD
These medications mimic the activity of natural hormone glucagon-like peptide-1 (GLP-1) receptors located in the pancreas, brain, and gut to slow gastric emptying, increase insulin secretion, reduce appetite, and improve blood glucose levels