How many US films in the 30s and 40s had transgender themes that were suppressed post-code (or were realized pre-code)? I wasn't under the impression transgender had made much of a pop culture impression until Christine Jorgensen in the early 1950s. The Hays Code did have provisions against overt sexuality and "perversity" which probably would have kibboshed transgender storylines (although a docudrama might still get through, like Wood's Glen or Glenda), but I'm just not aware of anyone trying to make a film about the topic until Jorgensen made headlines so am curious as to what examples I'm not aware of.
The CCA was driven by new media fears; Frederick Wertham had spuriously connected juvenile delinquents who read comics and, discounting the fact that over 90% of kids in the city read and traded comics, declared comics as the common factor. It wasn't helped when the Brooklyn Thrill Killers were dropped into his lap. Oddly though, everyone ignored him when he began the same campaign against television. Many of Wertham's accusations about comics have been transferred over the years to any new thing kids seem interested, heavy metal, rap, video games, etc. However the CCA was also a way for comic publishers to hurt their competition. Archie, National, Atlas, etc., set rules that specifically targeted the best selling comics from EC and Lev Gleason.