Given the social nature of stand-up comedy, specifically given the social nature of writing jokes for physical delivery to a group of humans, to me the term "anecdotal evidence" doesn't exactly apply to the somewhat scientific nature of jokes, and the scientific nature of the wording of jokes.
Does this community accept spoken word specifically comedic sources for information? For example, the american Louis C.K. may have reached a conclusion about evolution in a specific written joke that he applied to his TV show now available in link form here, and this joke can be exactly written here. Can this joke be a piece of /r/AskHistorian answer or question evidence?
No, I don't think that something a comedian said in a monologue would be considered an acceptable source here, but it could be an acceptable basis for a question. We have, e.g., entertained questions about assertions made in a Saturday Night Live skit by a comedian.
Our rule against using personal anecdotes in an answer is generally applied to people saying "I remember when I was a kid ..." or "well, my grandpa was in the war and said ..."; we just can't verify that information. You can find further explanation of the anecdotes rule here. The reason something said in standup wouldn't be considered acceptable is the same reason someone posting "my professor said once in a lecture ..." wouldn't work; even if we can verify that it was said (which is probably easier for standup than for Professor X at State U) we don't have any context or understanding of where the information comes from before it was said. That's the main reason we prefer to see primary sources or well-respected academic sources used as the basis for answers; those of us on the mod-team are familiar with literature in our areas and if it's outside our expertise, we can usually track down the sources in a library or online database to get an idea of whether they're reputable or not.
The only time you should ever be citing a joke here is as a primary source about the culture or people involved. One might cite a line from one of Bob Hope's USO shows to dispatched troops as evidence about public opinion on a war. Likewise, you might use an SNL sketch to discuss the media's reaction to Reagan's election. We have no format for how you do so- a YouTube link is sufficient for public media.
Beyond that, content or conclusions from jokes have no place here. If a comedian uses a fact, there are better places to cite that from.
If a comedian makes some kind of conclusion, as you mention, it's not as quickly cut and dry, but there's still no doubt in the end. Even if comedians were considered expert sociologists, no routine is peer reviewed. The entire point of citations is verification. Though they might not be anecdotes themselves, they are typically based on them; anecdotes are inherently unverifiable. Comedy routines are also not peer-reviewed at all. Nobody's going through Louis C.K.'s routines beforehand to make sure they are ethnographically sound observations. You might use one of his quips as a joke to being an answer, but it should never ever be used as evidence or a supporting argument.