I saw this thread bumped from 1999 and was all set to report a spammer. But ARAMCObrat posted relevant and well-sourced information that directly answers the question. Welcome aboard!
Pedophilia has a long history as a subject in the arts. You’ll find tons of it in ancient and Renaissance literature and paintings, often with a rather liberal and permissive tone. It might have been a sensitive topic to talk about in the 1930s, but it was certainly not so alien as to be unthinkable to those audiences.
I remember my grandma who was born around 1910 singing this song:
Warte, warte nur ein Weilchen
Dann kommt Haarmann auch zu dir
Mit dem kleinen Hackebeilchen
Macht er Hackefleisch aus dir
Wait, wait only for a short while
Then Haarmann will come for you too
With the little meat chopper
He’ll make ground meat out of you
Of course this scared us kids and we asked her who Haarmann was. She soothed us “Don’t worry, he’s long dead and did his deeds a long time ago, before the war”. But it shows that such atrocities by serial killers were very much present in the Weimar society.
It’s not for children, but Randy Newman had a song about Peter Kurten:
In Germany Before The War
There was a man who owned a store
In nineteen hundred thirty four
In Dusseldorf…
A little girl has lost her way
With hair of gold and eyes of gray
Reflected in his glasses
As he watches her
A little girl has lost her way…
We lie beneath the autumn sky
My little golden girl and I
And she lies very still
I guess not every sadistic murder involves rape and/or pedophilia, but generally that seems to be the pattern.
There’s the allegation, for example, that Freud deliberately knowingly made up the whole thing about Oedipus complex and Electra complex. He found it easier to claim that his patients were remembering fantasies rather than admit that there was pedophilia also going on in some of the upper class households in Vienna, even though he recognized the trauma was from early childhood molestation.
However, I think the revelations in the news about child abuse over the last many decades, and the fact that it had been generally hidden or ignored or deliberately overlooked, has made people today far more suspicious than people were a century or more ago.
I haven’t seen the movie in a long time but I am surprised now that the killer wasn’t identified as a pedophile, I thought that was a clear impression made in the film.
Either that, or else nobody dared to talk about it in polite society. But it’s probably the former. My evidence: the fact that the early Shirley Temple movies were made in the same timeframe.
(For those of you who don’t know what I’m talking about: go to Youtube, and watch any of the “Baby Burlesk” videos.)
Most likely, audiences knew full well what was going on, but the subject was considered too horrific for explicit presentation in a movie.
Subtlety does not equate to naivete.

My evidence: the fact that the early Shirley Temple movies were made in the same timeframe.
The novelist Graham Greene got into trouble at the time for discussing what she was asked to do in - shall we say, very adult terms, maybe precisely because he had brought into the open what most people preferred not to think about:
The Cafe didn’t exist when this thread was created, but that’s where this thread belongs now.
Moving thread from FQ to Cafe Society.
But, but…did @Flora McFlimsey and @Ukulele_Ike ever hook up?
Well, they (and others from the NYC area) did meet back in the dopefest era, but it wasn’t a ‘hook-up.’ For some unknown reason, Flora’s posts are gone, but the person behind Flora created a *new board name, which many of us remember: Eve. (BTW, one of the few Dopers I’ve actually met IRL.)
Back in the old days, the rules were somewhat looser about multiple screen names, and this thread was only six months after the board moved off AOL and let all the internet riff-raff in (including yours truly).
For what it’s worth, here’s my personal take: I first saw “M” about ten years ago, as someone born in 1968 and with a current mindset, but it was clear for me that Peter Lorre’s character was not only a child murderer, but a pedophile. What clinched it for me is his defense speech in front of the tribunal of the underworld crime gangs, which I remember best of the film because it was such an outstanding scene. In this speech, he says (paraphrased) “You are doing your crimes for petty financial gain, but I? I can’t help it, I have to do it! How could I do otherwise?” This strongly pointed to a sexual motive.

It’s not that the subject was too sensitive; it’s that it was too alien.

Pedophilia has a long history as a subject in the arts. You’ll find tons of it in ancient and Renaissance literature and paintings, often with a rather liberal and permissive tone. It might have been a sensitive topic to talk about in the 1930s, but it was certainly not so alien as to be unthinkable to those audiences.
I came here to agree with these comments. Pedophilia was certainly not unknown before our era. It was just handled more subtley in the movie.
Oh it’s @Eve! I should have guessed from the Algonquin reference.