The more specific question could've been "why were Warner Brothers' 'Censored Eleven' made and why did white people find them funny?" but I wanted the question to apply to all racist media at the time. What did white people in the United States find so funny about making fun of black people? It's often said today that most (emphasis on most) successful comedy usually comes from a place of hitting "upward" instead of "downward". So what did people at the time find funny about ridiculing a persecuted minority in American society?
Not my area of expertise, but having been on imgur, I'm not sure you need to specify 30s/40s
If you really want to destroy your ability to ever laugh again, you might consider looking into some humor theory, like exclusion or the superiority theory. Ridicule is kind of like anti-empathy. It's a way of saying "I am better than this person" and is especially necessary in a system without social equality. Rather than face uncomfortable questions like "do I actually deserve the preferential treatment I receive?" mockery becomes a way of perpetuating racial stereotypes and is particularity insidious because humor marks itself as a topic outside of real examination. Perhaps you have had a moment when you have seen someone offended by a joke who the joke teller than tries to placate or exclude by saying "you just didn't get it" or "you're taking it to seriously, it's only a joke"? And yet those jokes perpetuate and ingrain stereotypes that have a real affect on how people perceive the world.
tl;dr Don't study humor theory unless you want to have every laugh followed by a bout of intense self-doubt and over-analysis.