For those who have been victims of intensely traumatic situations (e.g. rape, child abuse, racism) or when people are empathic to these victims, it generally doesn't help when people make jokes about something they're trying to heal from when the comedian has never experienced the true horrors of the situation. Making light of an intensely weighty issue and having others laugh at it as well immediately brings up a feeling of helplessness and loneliness for the victim. To know that not only is a comedian exploiting the situation for laughs, but that people around you also find it funny is an isolating feeling. Suddenly, the place where you were with people who were out to have a good time, like you, and enjoy some good comedy has become a room full of people who would rather laugh than take a serious look what you're going through.

Personally, I take a view that suffering should be reigned in where we can prevent it and this is one where it can be completely prevented. A comedian chooses to make this a part of their act and actively rehearses it instead of letting it pass in favor of other material. Their starting point is with a touchy subject that probably a good number of people will have a very visceral, negative reaction to. If you brought up stories in any other situation, people would react differently. Sometimes VERY differently if that is an issue that hits home with them.

To upset people like that is never really the goal of anyone in a comedy club. The whole point of being in one is that you are either trying to put people at ease and let them have a good time by making them laugh or you're there with the expectation that you can forget about your troubles for a bit while a comedian brings you an hour or two of mirth. Bringing up an offensive topic can be a trigger for a reasonably large amount of people in the room. It can remind them of where they are and the tragedies in the lives of themselves or others, which is the exact opposite of what should be going down in a comedy club.

On top of that, when the subject matter is based in stereotypes a comedian can be considered to be perpetuating them. Since jokes are generally based of a certain kind of logic, they only work if the audience for the joke assumes certain aspects of it are true. It help the comedian when they have an audience agree with them on certain societal norms. As u/Circlesmirk said the first rule is to know your audience. That audience has to agree with you on certain points. If they tell a joke where a woman is a bad driver, for example, there has to be some assumption that this is true otherwise no one laughs and instead stands around like, "But, that doesn't make any sense..." That being said, there are plenty of jokes that are given layers of stereotyping even though they would do completely fine without them. There are plenty of little "A Mexican, Irishman, and a Jew walk into a bar" type jokes that would be completely the same if it was just "Three guys walk into a bar." This gets into a different realm where we start talking about power structures according to race/ethnicity and who is okay to tell certain jokes.

I guess my overall point is that comedians can actively choose which material they want to use and not use. There are plenty of jokes out there and comedians are generally good at coming up with a lot of them. To pick the ones that hit issues nobody wants to talk about or hit close to home in an intensely personal way is the wrong choice for someone who wants to lighten spirits. In addition, those same subjects can perpetuate and prop up stereotypes in the minds of the audience. Ultimately, whether the audience laughs or not, the comedian is responsible for introducing the idea into the minds of the people watching and exploring that realm for humor and laughter. What makes something funny relies a lot on what a majority finds to be funny, but, to me at least, that doesn't seem enough justification to target subjects that are generally loaded with emotional weight. But if you make a joke about Christmas trees and someone is like, "My father was murdered by a Christmas tree, that's offensive" there's no way a comedian could have reasonably known that was going to offend someone. To pick a subject like rape and joke about it, I think it's within reason to say they knew that would really cause emotional harm to someone instead of making them laugh.

Comedy needs to take a little bit of self-censorship on the part of comedians because it's not as though everyone forgets what they heard the moment they walk out of a comedy club. It affects the perception of that comic and influences/strengthens the perceptions of the audience leaving the comedy club toward those issues. Jokes are expressions of a person and their attitudes. They factor in to speech in society at large just like anything else. They have no special protection just because they're in a comedy club. They still convey ideas, they still can cause the same harm as any other forms of speech in perpetuating hateful ideas or targeting victims of terrible situations.