If you are over 50, are jumping jacks harmful to your spinal discs?

Not if you are in good shape. 

Older adults swim often because swimming is low impact. 

I don't know if they're harmful, but I would assume that any high-impact exercise could compress the spine and ultimately cause or contribute to harm.

Older adults seeking cardio often row, cycle, or swim. If your knees are bad, the first two can be problematic if you can't flex them deeply enough without pain, but even people with really bad joints can swim. They can also try stair climbers, elliptical trainers, and ski machines at the gym  (as well as rowing and cycling machines).