Some Like it Hot came out in 1959, and is about two guys who disguise themselves as women to hide from the mob. It did gangbusters despite not being approved by the Hayes Code, and is considered today to be an all time classic.

Never seen the show, but isn't this an instance where cross-dressing is seen as a gag and not necessarily an acceptable and normal thing to do?

As a needlessly serious answer - conservatives don't mind exceptions. What scares the shit out of them is any systemic challenge to The Hieararchy.™ Guys in dresses as a punchline doesn't ask them to reconsider how men and women are treated differently. Like asking why there's a female-only residence in the first place.