Basically, Conan O'Brien has this running gag called "Conan's Tabloid Moment" where he decides to stage a scandalous scene, take a picture of it, and sell it to the tabloids. At first, he pretends he's at a strip club. Then, he decides that the situation would be worse if he's drunk. What could possibly make that scene any worse? If the strippers were "trannies" of course! Because viewing cis women as sex objects isn't sickening, but if they're trans women . . . . And the way the cis women strippers become trans is by slapping a Keith Hernandez mustache on their faces. It's not that simple, Conan, and it's so not funny.
Conan has played around with gender on his show. A running joke of his is the fact that he looks a lot like Oscar-winning actress Tilda Swinton. A few years back, Conan enjoyed fame in Finland, and he attributed it to his resemblance to their president, Tarja Halonen. With both jokes, Conan made sure the joke was on him. He wasn't saying that Swinton and President Halonen looked like men, but that his red hair, pale complexion, and thin physique made him look like those women. He seems to be quite comfortable with his appearance, at least enough to talk about it and make fun of himself. But not everyone is as comfortable with the body they were born into. Trans people aren't afforded the privilege to feel comfortable in their own skin and be accepted as they are. That oppression shouldn't be exploited for cheap laughs.