It depends. Lots of people have back problems, spinal fusions, etc and still skydive. The opening of the parachute can be quite hard (not usually), and it can also cause a whiplash effect. Also, a parachute landing could be on your butt, kind of like sliding in on your rear end, which can also hurt your back.
So if your back has instability problems where this type of force or motion could affect it, then better safe than sorry. Most skydiving centers are able to help answer questions if you can explain your specific back issue.
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