It's a very mild skit that pokes fun at extreme sensitivities that sometimes dominate discourse online and in person. When the girl at the beginning says, "Don't clap - it's insensitive to those that don't have arms" she's not making fun of those wihout arms but rather those that would get upset at that sort of a gesture being considered insensitive. I mean, the closest it gets to genuine mean-spiritedness is the joke about what gender their baby is. And again, it's not making fun of a child that may grow up to identify as a different gender, but the mere fact that the parents don't want to be so presumptuous on behalf of the child to simply tell the natives what sex it is.
I mean, I'm not a fan of Kimmel. Compared to Kimmel, I think Fallon is probably Craig Ferguson-tier. But it's hard for me to see much to be offended by with the skit. Extreme sensitivity kills discourse just as easily as extreme apathy to those around you. The skit is lazy and unfunny, but I don't see anything malicious in it.