It doesn't transfer as well as people think it does.
The basic problem, as has been mentioned, is that one teaches head first, one feet first. Twisting technique, arm technique, take off and hurdle steps are different. You need to travel away from the board, which is not ideal in gymnastics (and why trampolinists don't transfer as easily as you'd think- they've trained to return to the cross.
At low levels you can get away with it, and it can be useful for cross training, so you're not putting low level gymnast/divers through high hours in a specific sport. I'd say really it's only advisable to continue with both until more than one somersault is being taught, and before any twisting somersaults. So once you're doing 1.5 + in diving, or 1+ in gymnastics, or flipping vaults.
Gymnasts don't transfer as easily as expected once they retire either- the muscle memory for putting feet/arms out can be too strong. Also it can be difficult to overcome the desire to arch when going backwards! The "rip" technique to enter the water is hard to learn.
Amy Chow I believe is one tried to make the US team after gym, but never made it. Most gymnasts who transfer successfully do so before the age of 11.