Okay, I clearly used "banning" as a relative term. Certain stations have stopped the play of the song, which has nothing to do with government or censorship. Of course private and for-profit stations will play what their listening public will allow.
However, coming from the late 80's and early 90's as far as my listening to radio goes, "Baby, It's Cold Outside" has nothing offensive going for it when compared to songs that were my contemporaries, like Used to Love Her by Guns n Roses or Sex Type Thing from Stone Temple Pilots. That's not to say that either of those songs should be normalized or accepted, just that "Baby, It's Cold Outside" was written by a husband and wife team, and the original parts were labeled "Cat" and "Mouse". It was clearly written as a "game" and intended to be funny. And FWIW, when the song was written, it was VERY common for people, when realizing they'd been speaking out of turn or acting out of character to exclaim, "What's in this drink?!" as a funny excuse for their behaviour.
While I can see the "sinister" side of the song when viewed through today's lenses, I do NOT see it through those same lenses when hearing it. It was intended to be funny and fun, not sinister and date-rapey. Again, I guess it all has to do with what a station's listeners will allow. But, as a PP mentioned, then a whole lot of rap music, or even "popular" music from a different era (i.e. 70's and 80's) would have to not be played as well.