I don't actually think the sleeping thing is an issue, it's more the insidious nature of being with a group of kids week in, week out, where opportunities present themselves.
I work with young people. I make sure that if, for example, one of them needs to go to the toilet, and I need to accompany them to make sure they don't wander off/get lost, I stay outside the block in full view of everyone outside. If there is a problem, I fetch another adult so neither of us is on our own with the child.
When I had a male colleague who ran workshops for teenagers, girls and boys mixed, we made sure he was never on his own with them - we set it all up so I could be an extra adult present while still getting on with my own work. We did it not because I didn't trust him but because it seemed like good safeguarding measures and it served to protect him from unfounded accusations.
Someone who was trans and wanted to work with young children would presumably do the same sorts of things so there would be no issue. I'd have no problem at all with this. I wouldn't expect to be told because I'd assume they were doing the sorts of things that protected both the children and themselves, as I do.
However, it would be so easy, if you were so inclined, to say 'I am a woman' and have access to young girls, and then to not put any of these measures into place. Volunteer at Brownies, go week after week, young child has problem with clothing, into the toilet to quickly 'help' them - now what? Anyone, trans or not, who has no interest in abusing little kids, simply will not put themselves in this position, or if they end up in it, won't take advantage of it.
But there will be some who will deliberately put themselves in this position, and then take full advantage of it. We know it happens. It happens in Scouts. These are not always people who like little girls by any means. What they can now do though is to say 'I am a woman' and access girls as well. Scouts have had major issues with it. It doesn't mean all scout leaders are paedophiles. The church has had a problem. Football has had a problem. Hardly any priests or football leaders are paedophiles. Which is no comfort to those who are abused by the handful who are. So far, Brownies and Guides has been relatively well protected because the most likely people to be sex offenders, men, could not access it.
Maybe before we throw open a space which up until now has been relatively safe, we need to look at why these organised spaces have not been safe for some kids in the past. Learn any lessons. And we need to make damn sure that someone with predatory intent couldn't do the same thing in Brownies.
It's not about hating trans people. It's about someone who actually isn't trans at all using 'trans' as a handy word to get access to young girls. I don't know what the answer is. I do know that if my daughter was exposed to someone who was trans who just got on with the job, (assuming I even knew, and I probably wouldn't) I'd be more than happy. Any decent person who can teach my daughter something is fine by me. If she came into contact with the 1 person in 10,000 who abused the system, and she came to harm, I would be ready to commit murder. And the fact that trans people are not the problem and that it was just the bastard exposing a loophole would be no comfort at all.
It is not transphobia to understand that abusive people will exploit a situation. So, how do we let trans people live their lives without creating a system for abusers to exploit? A nightmare question but I think it is the one we have to answer.