Terribly sexist but I'd assume the average 20 year old babysitting strangers for kids, the female would probably have more experience or want to do it for work experience, whereas the male would just do it for the money so I'd pick the female. And of course in there is a lurking fear of strange men, because that's how we have to be in all areas. Would I prefer a male or female taxi driver if I was totally pissed at 2am? Would I rather be followed down alley by a man or a woman?
But what about parents? Men abuse their wives and children statistically more than women do. Do you allow your husband to be alone with your children? Would you let your DB or BIL etc babysit? Do you think all men should be barred from all schools? We have a male caretaker and a male music teacher, is that an unacceptable risk for our school to take?