It isn't any different from racist jokes, and Chappelle makes his fair share of those. My only criteria for comedians who make jokes on sensitive material is that they do it fairly. I don't believe it renders him immune to criticism, that's silly. He's a comedian, they pretty much live off criticism.
But I also don't believe that living a magical world where nobody makes jokes about sensitive things is very helpful either. Dave Chappelle could never make a trans joke and transphobic people would still be just as vicious. But you don't have to be transphobic to laugh, either. Some people can take those jokes, some cant.
I personally think it can make you stronger to be able to laugh at such a thing -- if you can't face the criticism in the form of a completely impersonal comedy show, then how do you expect to face it in real life? There won't be an internet mob to defend every victim of a sensitive joke, nor will there ever be some free speech rule that prevents people from making them.
Trying to censor comedians is pointless to me.
Being able to laugh at yourself is great, and Cappelles humour often succeeds in doing that. But that's such a fine line to walk, and his transphobic jokes are nothing other than transphobic. There isn't satire there, or some hidden clever message, it's simply dehumanizing and I'd imagine insulting.
Insults have a lot heavier weight than many people like to think. It's not just a case of having "thicker skin" or being able to laugh at yourself. If your at a stage in your life when your brain is in heavy development (childhood,teenage years etc, the years in which bullying tends to happen the most), insults will have huge lasting effects on your psyche. When a comedians jokes borderline on insults they're no longer jokes anynore.
Like for me, when I hear "faggot", it's not a matter of having thin skin or simple being just offended. It's a matter of having heard the word through out my life, more than enough to do me for the rest of my life. It then becomes about taking that word out of people's common vocabulary so that future generations of gay kids might have to endure it less.
I can shrug off the people of the world comparing my relationships to man fucking a chair and calling all of us kiddy-fiddlers (common jokes in old comedy shows). But it's fine, because fewer people speak like that than ever, and I have it pretty good in the grand scheme of things. Transgender folk though, they face even worse comparisons like that every day. They have the thickest of skin out of all of us.
Chappelle segments on transgender people and so called "jokes" (insults in disguise) directed at that group do nothing but harm imo. When you see someone occupying a public stage like that, making those jokes, I think it's incredibly important to call them out for it. We're not even close to a point in time when we can debate the acceptableness of making transgender jokes. Suicide rate is ridiculously high in young transgender teens in part because of how socially acceptable to is to make fun of them and how little support they recieve.