Should baby boys be bathed/cleaned by only men, and girls by only women?

I was in the baby aisle at the supermarket today and overheard the conversation of the women behind me. One of them said she needed to speak to a pharmacist for advice on nappy creams because her sons tinkle looks especially sore, and her friend was just horrified and said that she would never even think of touching her sons private parts as it was “awkward and inappropriate to touch a little boys penis”. She said that her son was bathed by her husband and her daughter was bathed by her only as she didn’t think it was right for a man to be cleaning her down below. The firsts lady replied that the way she worded it makes it sound like there’s something else to it, but that plenty of people had “seen and touched, for lack of a better word” her sons privates as her family and day care obviously do their fair share of bathing and nappy changing.

I think her phrasing (“touching”) has bad connotations and I guess there’s not a nice way of saying it, so while I agree that I would never “touch” my sons privates, I don’t know how I’d get through the day without moving things around a little to ensure he’s properly cleaned etc. What do you think?