'And aren't parents with something to hide, going to just "disappear"? '
^^^ Not in my experience but that's obviously limited. And as HC says, they can often be wonderful parents in every way except for this procedure; you know, doctors reporting good interaction with mum and dad etc. It's a really tricky area and unless the parents are also abusive, I would be concernd about sending good but overwhelmingly misguided and stupid individuals to prison.
And yes, probably it's not as bad as you're imagining. Children having genital examiantion (along with paediatric assessment, I can't stress enough that we examine the whole child, not just get them in and ask tehm to whip their bits out :c) can be supported by play specialists so the whole thing is fun, their parents are in the room with them. It is done by paediatric doctors who are geared up towards children in a a pediatric setting (so lots of colours and generally not the crap waiting rooms we're used to) and that should be the bloody standard everywhere as far as I'm concerned. Examinations are not carried out on screaming or frightend children but their fears are explored to see if they can be allayed.
If you're an older child/adolescent then you can give your own consent or not for an examiantion anyway, I think it's called Fraser competence now but I used to know it as Gillick competent but I believe this has now changed.
Maybe the answer really is that all children should be routinely examined at various ages regardless of colour, creed, religion, sex etc so that all children are familiar with the process and it becomes a part of our culture like immunisations. I honestly don't know.