Why has this turned into a discussion about gay and transgender issues and acceptance? A young boy saw something that he didn't understand and panicked. Simple as that.
Because it was 1993, not 2016, and he was a kid. Transgenders weren't the "hip" thing at the time. He also wasn't sorry that he just assumed Mrs. Doubtfire's gender.
CDEGFEDCC. (Shhh!)
It would be (and still is Illegal) for man to dress as a woman in order to get a job (pretending to be a woman). Especially looking after children.
Let Zygons be Zygons