Critic Andrew Sarris defined the screwball comedy as "a sex comedy without the sex." His Girl Friday knows that sex exists; Walter is concerned that Bruce and Hildy may have sex on the train to Albany until he hears that Bruce's mother is going to be going along.
WALTER: That relieves my mind.
HILDY: It was cruel to let you suffer so.
But why is the film so concerned about Walter suffering? This is a sophisticated comedy about irreverent adults. What's up with making sure Walter, and the viewer, knows that no sex will be happening? Why's Walter made of such delicate stuff?
A big part of the reason is the Hays Code. The code was adopted by the motion picture industry in 1930. It declared in part, "No picture shall be produced that will lower the moral standards of those who see it." That meant no traveling to Albany with Bruce without mother coming along for the ride. (Source)
And it also meant that all other references to sex in the film are super-buried. One of the newspapermen, Stairway Sam, is so-called (if you watch closely) because he looks up women's skirts when they go up the stairs. And Mollie denies she ever slept with Earl. But that's about the extent of it. You're not even allowed to hear that Mollie is a prostitute in the film (although she was in the play).
The violence in His Girl Friday is also low key. The worst moment is when Mollie throws herself from a window—but the film is careful to tell you she survived.
You could easily imagine a racier, franker, version of His Girl Friday. But thanks to the Hays code, it's pretty much sanitized. Watch this with your little nieces and cousins… or, better yet, watch this with your grandparents. They'll love you for it.