Cinema is considered an inherently conservative medium. That is to say, it is easier to use it to maintain the status quo, however, that does not stop filmmakers from challenging the societal expectations. The Hayes Code, a set of rules on what was and was not considered morally acceptable to show on film, became strictly enforced after 1934, leading to a lot of films becoming censored to be seen as "fit" for audiences, at least until the early 60's. The films are ones where censorship was present and enforced, if not challenged. We can see throughout history that censorship and hiding the public from "scandalous" things will not erase them from existence, but the current state of affairs show we have not learned that lesson fully yet.
Examples:
Imitation of Life 
Imitation of Life's script was heavily scrutinized and rewritten in an attempt to keep the movie "morally pure" for audiences at the time. The elements of interracial love were seen as "dangerous" to the public, and was in violation of the code. The movie ends up taking a different ending than the novel it was based on, and scenes highlighting aspects of racism from the time were cut from the movie.
She Done Him Wrong
Mae West's controversial performance and line delivery predates the Hayes Code, however, that's not to say there were not complaints. She Done Him Wrong is shown to scare the world of cinema at the time, showing what could happen if a powerful woman steps into the scene, and censorship was not there to regulate and control women's bodies.
The Last Laugh
This still from the Last Laugh shows the concept of censorship in play. The only title card for the entire film, it's suspected the ending was changed for American distribution to provide a more "happier" ending, leading to believe the fate of the former doorman was meant to be grimmer.
Scarface
While the reception for Scarface was seen as generally good, the movie was banned in many cities and states due to its "glorification of crime"
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