I was brought up naturist, and decided it wasn't for me when I was about 10. I think that naturism needs to be done carefully, but it is up to the parents and experts, not us, to make sure that happens.
I'm aware that this will probably make some people not read the rest of my post, which is a shame, because I'd like to try and get to the bottom of some things we can all agree on.
Firstly, naturism IS a safeguarding issue. It's a family activity, like camping, and family campsites also need to do far more to prevent abuse in my opinion. It's also a very small community, and that means coverups would be much easier, and a sole charismatic figure could easily have too much sway. That said, since reading through this thread, I have found that the NSPCC have oversight of naturist safeguarding, which is good and should prevent this from happening.
Secondly, having groups of men outside naturist events shouting at the people going in is totally unacceptable. They will be terrifying the children they are supposedly there to protect. It also puts naturists on the defensive, when we need them to be open, working with the police, publicly showing their safeguarding policy. I've seen people saying "why were the men covering their faces as they went in!?" as though that shows they're guilty. I'd cover my face if you shouted at me and filmed me in public! The whole protesting thing promotes secrecy and fear when we need openness.
Finally, on parenting, I've read stories including here where naturism has been part of someone's abuse, and stories where naturism has been good for someone. In all those cases, the key factor is the parent or parents. If you think your child fears you, or could not openly say to you "I don't like this", then you shouldn't do naturism, end of. I did feel confident to say that to my parents, and as a result even though naturism was not for me I did not get harmed by it. Some people are saying a child may not like it but not feel able to say so, and I think we can all agree that is a recipe for disaster.
How can we tell which parents are abusive and which aren't? I don't know. I don't think we can. If parents ARE abusive though, then I don't think banning naturism will help. They'll just find another way to abuse their child, and you take away something which non-abusive parents could be bonding with their children over.