Here's a suggestion which might solve the problem, although it would create more expense for the competition companies so they most likely would not do it. If photography is allowed at the event (I know some competitions don't allow photography at all), and the competition companies were to issue a "parent photo pass" that you had to acquire prior to the event and display, they could quickly identify who is a parent taking pics of their kid and who may not be. It could be a badge you pin to your shirt or something. This way only parents would be allowed to take photos. Just a thought, although it's not the most practical of solutions.
At our regional and national competitions we have photo rules:
Every team/newspaper can fill out a form for a photographer, that will be allowed to take pictures with high quality cameras with zoom objectives (not sure if it's the right word).
They get a registration number and a button, but it's not for the person especially, but for the team, so it is possible to change the photographer for different events, but they will still know which gym he/she is from.
Everyone else is allowed to take fotos with their mobiles, ipads or small cameras without big (quality) zoom.
We don't have VIP areas where parents or fans can see the performance near to the stage, in front of the stage are only the coaches and the registered team photographer.
At the entrance, the security checks bags and everything and won't let you in if you have any photo equipment that is not allowed for fans and parents.
I'm sure some creepy people will still find a way, but it is a step in the right direction.
Video taping is not allowed and the security is trying to enforce this rule.
The coaches still videotape their own routine.