I am a male Beaver leader. Now admittedly I identify as male, so not the same issue.
We take girls on camps and sleepovers, as well as boys. We have robust safeguarding procedures in place to protect everyone. Mostly common sense, but we stick to it firmly. Why wouldnt you?
Sometimes Beavers do need to share sleeping space. For example a hall that oy has one room for the Beavers and one room for the adults. Adults never share with children - full stop. They will always have private areas to change, wash etc. Its just the lying down and sleeping bit that is sometimes mixed. Again, common sense. Its not gender specific either, we make sure boys can access privacy from other boys if they wish, for example.
And as for adults helping children shower as mentioned above, its not going to happen. For goodness sake! Of course if a child with additional needs is with a known carer (usually a parent), but we apply procedure there too.
The thing is that gender and sex need not and should not be an issue if the correct procedures are in place. That goes for both adults and children.
I also coordinate the DBS applications for our group. When a new adult is DBS checked, their previous identities ARE checked too. In fact I can tell you that previous forenames is one of the questions that the DBS asks. If a person lied about this it would soon be flagged up (the DBS knows more about us than many realise).
Please volunteer to help your group if you can. They should welcome the support. I would say to be prepared to be treated as a leader rather than a parent though. We had a parent who tends to stick their own child and we had to nip it in the bud.
Sorry that this post has a negative tone. It is just so demoralising when we generally care so much about what we do only to have it thrown back at us.