In the American version, the story of three tradesmen (the butcher, the baker, and the candlestick maker) all hanging out in a tub seems like it might be progressive in some ways. That version is warped from the original, which goes, “Hey, rub-a-dub, ho, rub-a-dub, three maids in a tub. And who do you think were there? The butcher, the baker, the candlestick maker, and all of them going to the fair.”
According to an NPR interview with a London librarian, even back in the 14th century, British tabloids loved hearing tales of the well-to-do caught up in scandalous affairs. And so this song we sing with our children, which has spawned many bath toys, actually tells the story of upper-class tradespeople hanging out at a fair and getting caught checking out a bath filled with naked ladies in it. Relatedly, 14th century fairs seem more edgy than I’d imagined.