Is it normal for all or most older women to test positive for an autoimmune disease?

Autoimmune: Autoimmunity is an immune response directed against an antigen normally present within your body. Autoimmune disease is a pathologic condition. There are multiple tests for autoimmune diseases. Some screen while others confirm the presence of disease. It is possible to screen positive for a test but not have the disease hence further testing is done to confirm.

No: No, this is not common. Just being older and female does not mean you should be any more likely to have positive autoimmune disease test results.