I think AstraZeneca is wrong about the immune reactions it is seeing in trial participants.
Both transverse myelitis and multiple sclerosis have been related to vaccination. I will have to dig regarding transverse myelitis but I think it may be on the US table of vaccine injuries.
As for multiple sclerosis it does seem there is a causal link. This makes sense as vaccines are designed to produce an unnatural immune response, which is what "auto-immune" diseases seem to be (whether or not there are intracellular parasites involved is another issue).
Here are some links to published science on the subject:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4266455/
That article references this older work:
https://www.bmj.com/content/bmj/2/5546/210.full.pdf
As I recall lawsuits were filed in France for multiple sclerosis following Hepatitis B vaccination.