Yes when you suffer from stress and/or anxiety you can weaken your immune system and cause an autoimmune disease.
When you're suffering from anxiety and are stressed out your body releases a stress hormone called cortisol.
That stress hormone called cortisol is released in bulk all throughout your body which causes your immune system to get weak.
Stress and anxiety has also been linked to relate too things such as type 1 diabetes, rheumatoid arthritis and even Celiac disease.
When you suffer from stress and anxiety you'll also be more prone to get the flu as well and it may take longer for your body to recover from the flu and other viruses due to your weakened immune system caused by the stress and anxiety.