[Not because they want cover to tell problematic jokes, but because they want to be able to lay it out for other people why they shouldn't.]
Question: Why are *ist jokes a problem?
Short answer: Because they hurt the feelings of people who have done nothing to merit such pain, whether you meant it to or not.
Longer answer: Because they are based on either validating or making light of something that’s been used for a very long time to hurt a whole lot of people. The ability to remove that thing from its real world context and treat it only as a source of humor is a privilege some people have, and exercising it hurts other people. Further, acting as if one’s audience is composed solely of people who have that privilege marginalizes those people who might be in one’s audience who don’t have that privilege, which compounds the harm being done.
Quibble: But I don’t actually mean it!
Retort 1: Yeah, you do. You’re just not honest enough to come right out and say it, so you leave yourself an out by calling it a joke. If you didn't mean it, the fact that it's hurtful would be sufficient reason for you to stop. You’ll have to figure out if you’re lying to yourself or only to everyone else.
Retort 2: So what? Your not meaning it doesn’t make it any less hurtful.
Retort 3: There’s a real good chance that someone in your audience does mean it. Why would you want that douchebag to think for a moment that you’ve got his back?
Quibble: But people say mean things about Dan Quayle/George Bush/etc…
Retort: Making fun of the powerful and making fun of the powerless are not equivalent acts.
Quibble: But Jackie Mason/Chris Rock/etc. said something similar about Jews/Blacks/etc.
Retort: Members of a community laughing at themselves and members of the community that oppresses laughing at the community that they oppress are not equivalent acts.
ETA: Quibble: But there's no right not be offended!
Retort: This isn't about anyone's rights, it's about how to not be a douchebag. Choosing to hurt people for no good reason is douchebaggery even when no one's legal rights have been infringed.
I don’t have specific cites to point to for where I got these ideas, but I got them all through informal conversation between people working on learning to oppress less and with members of various oppressed communities. None of it is original, at most I've worded it a bit differently. If this piece is giving you any epiphanies, there’s a really good chance that a you heard it first from someone who is a woman, a person of color, LGBT, disabled, a religious minority, a combination of the foregoing, or somehow otherwise marginalized and oppressed in this society – only you didn’t have that epiphany when they told you.
It’s worth spending some time contemplating why that is.
 Thanks to marnanel for the quibble to add.