I can't quickly think of a joke that is not at someone's or something's expense. It stands to reason that someone will find that offensive and others from the same group will think it funny. When my wife first heard bad Asian drivers called DWO (driving while oriental) she laughed like when she discovered the Three Stooges (she was cackling). I'm sure that is offensive to someone.
The thing is, I've heard the best blond jokes from blonds and back in the day when white people didn't think themselves the same, Polock jokes from Polish people, etc. The offended are most likely to loudly speak, creating the impression that they are the official spokespersons for their group.
When a friend, a black man, said, "You know how I can tell when y'all are telling a n****r joke? He quickly turned his head to look over one shoulder and then the other. TRUTH in 1980 Georgia. Some wouldn't find it funny when they saw and knew it, but he knew I'd laugh "with him" without malice.
Trans people do have a special problem. Even with it's horrible history, it was easier for most white people to accept the basic humanity of black people and do their best to shed racist thought than to see transgenders as something understandable. We may do our best to be polite and accommodating but will we ever deep down believe that a person with functional overlies, and uterus who has a baby is a man having a baby? Trans people know that and it may have something to do with their aversion to jokes about it, knowing that many people think them a joke. And to be honest, I think that is pretty damned horrible. I wish it was not that way, but I think it is.
No matter what you do, you are offensive to someone. Killing off comedy and jokes won't fix that.