I would think that the warnings Disney posts may be a little too strong. However, they can't stop you frok going on a ride, but you have been warned.
I think that the safari ride is extremely bumpy; the road was created that way and the vehicles are built to shake you up.
A couple of years ago I had a kidney out; my doctor told me that for six months any signs that suggested people with bad backs or who were pregnant should not ride applied to me. I think he gave a tricter warning than was necessary, but I still followed his rule.
On a side note, you can take a "test flight" at Star Tours if the lines are not too long and they are NOT using all six vehicles. They will put you, and anyone with you, in a vehicle by yourselves and run the attraction WITHOUT the movement. I think it is also an option on Body Wars. Just ask when you get to the podium at the end of the loading area.