Ok, but statistically both women and children are more likely to be assaulted or raped or abused by someone they already know. Attacks by strangers make up only about 10% of all incidents (rapecrisis UK) and some of those will be carried out by the same individual. So, yes, men are still offending more, but it's more much more likely to be a man you know than a random trans woman in a bathroom.
I'm pretty sure there's laws about convicted pedophiles being around children.
Again, in the majority of cases where children are harmed by a pedophile it's someone that is known to the child.
Unfortunately there will always be 'first-time' criminals who it turns out worked with children, that's horribly sad, but unless you want to ban men (as they commit the most crimes) from working in schools or in places children might be you can't prevent those people, who have done nothing wrong before they do something wrong, getting access to their victims. We don't have a crystal ball, we can only act on things that arouse suspicion. But being suspicious of a person just living their life, is not helpful, it's actually pretty horrible.
Trans women are no more of a risk than any other strange man, and strange men are statistically safer than men you know.