Autoimmune disorders of any kind are certainly impacted by stress (which raises cortisol) levels, for sure. This is a problem for people without autoimmune diseases or things like asthma as well, but it is certainly harder on those who do. Here is some information from Science Daily. There is certainly more information out there that addresses the same thing. As I once had advanced Graves Disease (thyroid was removed almost 30 years ago), I've personal experience with this.

It is also good to remember that a thyroid-related autoimmune disease isn't really about the thyroid - it is really about the underlying disordered autoimmune system itself that manifested by attacking your thyroid. This never made real sense to me until after my thyroid was removed (it was no longer controllable), and 30+ years later I still have problems with autoimmune disorders. So far nothing as serious as the Graves though, for which I am deeply thankful.