Good question, I’m much more familiar with the oncology literature and there is definitely causative evidence linking EBV and to a lesser extent CMV with lymphoma/lymphoproliferative disorders (particularly in the post-transplant setting).
I believe the evidence for autoimmune disorders is much weaker (with the caveat that this is well outside my scope of practice), I’ve heard it being implicated in MS from my neurology colleagues but my understanding is it’s a weak correlation at the moment. I can’t offer more than uneducated conjecture on other autoimmune diseases. UpToDate says the following:
“One difficulty in proving a link between EBV and MS is that serological evidence of EBV can be found in 83 to 90 percent of adults in the Western hemisphere [99,101,102]. On the other hand, EBV seropositivity among adult MS patients is near 100 percent, significantly higher than healthy controls [91,102-106]. Additionally, children with MS are significantly more likely than healthy peers to have serological evidence for prior EBV infection, at an age when EBV seropositivity is much less common than in adults [107]. However, there is conflicting evidence concerning the presence of EBV in brain tissue of patients with MS [108-111].”