I hope Colbert has gotten better but both him and Stewart had a long sordid history of using transwomen's mere existence as a punchline.

I stopped watching Colbert before The Colbert Report went off the air, for reasons like this. I also stopped watching The Daily Show around the same time. I never followed him on network television, so genuinely don't know if he's any better or more fucking importantly if he ever apologized. To my knowledge, I've never heard of Stewart or Colbert making a long-winded apology to the trans community for using them as the butt of their jokes for an incessant amount of time on the Daily Show.

here, via archive.org is Tumblr's "Your Moment of Hate" which was dedicated to documenting the jokes in which being transgender was a common punchline on the Daily Show.

https://web.archive.org/web/20150215064620/http://yourmomentofhate.tumblr.com/tagged/The-daily-show

The author of the blog had this to say in a post titled "Why Stephen Colbert's Transphobic Jokes Are Not Satirizing Transphobia":

In each grouping above, one of the jokes is from Jon Stewart and one is from Stephen Colbert. Yet, despite the fact that Jon Stewart is a liberal comedian, they are almost indistinguishable from each other.

That’s the thing, jokes mocking and dehumanizing trans people are a liberal problem. Liberal comedians and comedy shows do it constantly. Nearly all of them. It’s borderline harassment.

Colbert isn’t using these jokes to mock conservatives’ transphobia, he’s just using time-tested trans jokes (ones often used by other liberal comedians) for easy laughs. And because liberals (as well as conservatives) find the idea of a trans person to be the most hilarious/disgusting thing ever, these jokes fucking kill.