Can menopause trigger autoimmune disorders? I was diagnosed with both psoriatic arthritis and celiac disease at 51.

Maybe. There is more autoimmune (AI) disease in older women, but it is unclear if it is related to time or hormones. Time: an AI condition is a problem in the immune system. The longer we live, the more likely a problem will develop. Hormones: women have an immune system that tolerates foreign things, that is how they have a baby. If that tolerance goes away, then there can be an issue. But exact cause?
Yes and no! . No relationship between celiac disease and menopause, but it is usually earlier in onset. Psoriatic arthritis and all spondyloarthropathies have a peak after menopause in women . I suspect the celiac dx!