Again, anecdotal, but my wife has autoimmune that attacks the thyroid, causing her to have 180 bpm heart beat (24/7). Doctors recommended medicine that further attacks the thyroid, but she went with a paleo diet instead, after a recommendation from my bio PhD sister who also has autoimmune. Her symptoms stopped within a week or two, her values are now back to normal. Could be something else, but I doubt it. She had the same thing 6 years ago and it lasted for 6 months, while eating this medication that damaged her liver.
Turns out gluten in particular is linked to many autoimmune diseases. Here are some shorter blog posts by the same author [2] on gluten, autoimmune and AIP.
Unfortunately there doesn't seem to be many large scale studies on diet and autoimmune, but personally, after understanding the underlying mechanisms better, and having personal as well as overwhelming online anecdotal evidence, I'm fairly convinced. I recommend keeping an open mind about this one and start reading.
[1] http://www.amazon.com/Paleo-Approach-Reverse-Autoimmune-Dise... [2] http://www.thepaleomom.com/category/autoimmune-2/the-whys-of...
https://www.amazon.de/Paleo-Approach-Reverse-Autoimmune-Dise...
It helped many people with diagnosed and undiagnosed autoimmune diseases and conditions.