You can tell a joke that makes fun of a group, if you are a member of that group. It’s allowed. You should not, no matter how accepted you feel you are by a group, tell a joke about a group that you are not actually part of. If you have no standing in a group, don’t tell jokes that make fun of that group. My mother and wife are Catholic. That does not mean I can tell Catholic jokes. I have several very dear friends that are LGBTQ. That does not mean I can tell LGBTQ jokes. I have no actual Standing within those groups so I just shouldn’t.
Chris Rock can tell jokes about African Americans, their culture, their situations, because he’s African American. He can even tell jokes about African American’s interacting with white people, as long as it’s from the African American point of view. Jacky Mason could tell jokes about Jews. He was not only Jewish, he was a Rabbi. If anyone could tell Jewish jokes it would be him.
I can’t tell either of those type of jokes. I’m not African-American or Jewish. (But believe me if I was both I’d have lots of material.) It’s not “unfair” or “racist, though I’ve heard both terms tossed around when this discussion comes up. It just the way it is. If you have standing, it’s fair game. If you don’t, then just don’t. This is where I see a lot of young comedians getting in trouble. They hear a great joke and figure they’ll use it. Setting aside the stealing/plagiarism question for the moment, if they aren’t part of the same group as the originator, it comes off as sexist or racist, or worse. If you are not Chris Rock, then don’t try to tell his jokes.
So what kind of jokes can I tell? First there’s a huge mass of jokes that are open to anyone: Schrodinger walks into a bar, and he doesn’t. Almost all of the material I have used over the decades has been bias free. Simply because I didn’t know who would be in my audience and I didn’t want to make someone who paid good money to see me, uncomfortable. Now, if I DID want to go ethnic I can do all the jokes that Jaki Mason or Chris Rock shouldn’t be doing. Jokes about white guys. Jokes about people in Minnesota. (Garrison Keilor has made a career out of that.) Jokes about being middle aged.
In the end though, I find it’s best just to avoid biased humour, or most religious humour, or humour based on stereotypes. Really any humour that makes fun of a person or group of people. Both because you don’t want to offend your audience, and because to be honest they aren’t clever. The familiar stereotypes have been around for years, decades, centuries in some cases. Nothing clever can be done with them any more. To try is stupid and lazy, and those are two things that will kill your comedy career faster than anything.
Now that’s not to say you can’t include recognizable groups in your jokes. You shouldn’t be afraid to add texture to your characters. That’s good writing. Just don’t make fun of them: A Priest, A Rabbi, and a Black Lesbian walk into a bar. the Bartended says “What is this, some kind of a joke?” See what I did there? I includes all sorts of characters of groups that I have no Standing in. But it’s OK because I did not make fun of them. I did not use any stereotypes. The joke is making fun of the joke’s own structure.
If you want to succeed in comedy, and let’s be honest we all are doing comedy because we want to be accepted, write your own material, about your own situations and put a clever twist on them. Don’t resort to tired stereotypes, they just aren’t funny any more. A clever, funny, really creative story about trying to assemble your grill, or waiting to pay your student fees, or getting your car fixed is going to go over a lot better than a string of tired stereotyped Black, Mexican, Jewish, Gay, Redneck, Liberal, Feminist, Obama, or whatever jokes.