And yes, assuming a man is likely to be a paedophile is grim and ridiculous, but in my opinion no more grim and ridiculous as assuming a man is likely to be a rapist
Yep, agreed.
But. Women are raised from childhood to treat men with caution. To keep themselves safe. To protect ourselves from those with the potential to harm. To not walk alone at night, etc etc, because sometimes men do bad things to women, and we know and are taught that those man can look like anyone, and that happens pretty often in our culture. And so we avoid certain situations, and in other situations we exercise caution, because you can't tell who the good guys are. And we size men up for potential risk, because we've been told that's our job, and because we want to be safe.
It's not nice for anyone, is it? It's not nice for men not to feel automatically trusted, and it's not nice for women not to feel automatically safe. That's the reality of living in a culture where sexual assault and rape are relatively common. Good men don't get a pass from the not nice bits simply because they are not the main recipients of the violence.
But here's the difference between these situations - men aren't denied employment opportunities because women exercise caution around men because some of them rape. However men are denied employment opportunities because some people 'feel weird' about the idea of male childcare workers and feel they are likely to be dangerous rather than simply potentially dangerous. So men are less likely to train for those roles, some employers are less likely to hire because their customers might be put off.
But the reality is we do the same sort checks with all childcare workers and settings as we'd do in evaluating a situation for the risk of rape or assault. We look at the risks involved in anywhere we leave our children and how they are or can be mitigated.