I found (maybe someone else has found it before) this Associated Press article from May 18, 1937 where Leon Schlesinger talks about censorship of his cartoons, both Hays Office censorship and self-censorship brought on by viewer complaints.
One odd thing is that the article says that Schlesinger stopped using scary characters "because, in one picture, he had a monster that was the heavy. The monster frightened the children -- as well as Porky the Pig -- and the letter of protest looked like a star's fan mail." I assumed he was referring to "The Case of the Stuttering Pig", with its memorably scary transformation of Lawyer Goodwill into a toothy monster, but that cartoon hadn't been released to theatres yet at the time the article was written. So either the writer of the article misunderstood, or there's another cartoon that was already in theatres and getting complaints, though I'm not sure which cartoon that would be. (If only because, before "Scaredy Cat" in 1948, there's no WB cartoon that's as scary as "Stuttering Pig.")