There was a parent on CB within the past year whose dd was in the middle of diagnosis. They weren't sure what specific autoimmune she had but was having issues with painful and swollen joints. If I recall, the gymnast was training L5. I will try to search for the member for you.
I am an adult with JRA, initially started as reactive arthritis. When I was little, the consensus was to avoid all sports as it would aggravate the disease but with all the meds available now and the research showing that more activity is better than less, and the consensus is to encourage sports while closely monitoring symptoms. The biggest issue for gymnastics is the intensity level both with hours and with physical impact from tumbling. If your dd can achieve medicated remission, then there shouldn't be any reason she can't keep going through the JO track. However, if she has flares, these will affect her ability to maintain and progress in her skills. In that case, moving to a lesser intensity track like xcel may be better or a less intense sport in terms of pounding. Honestly, it is too early to make a decision on this. Hopefully the meds will work great for her and she will have no other problems.
ETA: the other parent is tpmom and she is still active. If she doesn't respond here, you may want to reach out to her privately.