I don't agree with the petition. Satire is important. My wife and I have been watching a TV show called Community, which frequently features bigoted jokes about race, sexuality, gender, etc. And every time, the character making those jokes is portrayed in a bad light. I think this is a good thing.
Comedy is often the only context that taboo topics can be discussed openly. When comedians "punch up," making fun of the oppressor, they're using their platform to educate the public in a way that nobody else possibly can -- they make sensitive issues like this approachable and fun; they can make people think about their actions and teach good morals without making people feel bad about themselves.
There's two kinds of transphobia: informed and ignorant. There's no hope for informed transphobia -- those people are just going to keep on being ugly because they like punching down for whatever reason. Ignorant transphobia is altogether different: people who giggle when they see a "dude in a dress." Those people can be taught that their actions are insensitive. It's best to do so without polarizing the situation and labeling them as transphobes -- that sort of conversation produces informed transphobes! By satirizing transphobia, we can convert people who ignorantly express transphobic sentiments into people who (want to) refrain from doing so.
I had a conversation about privilege with some students a few weeks ago. One guy thought I was trying to make him feel guilty by talking about hate that I've experienced in public spaces (very carefully avoiding the word microaggression, but clearly communicating the concept). I assured him that I didn't want him to feel guilty, in part by saying "now, if I heard you say 'look at that f****** tr***!', then I'd want you to feel guilty." His jaw dropped and he said "no, I never said that!" and I agreed "No you haven't! So don't feel guilty!" He was immediately on my side. My statement was a deliberate choice: I came out to him as transgender in that moment, and I satirized the use of an epithet as an object lesson. Comedy works. It's one of the best tools we have.
On the other hand... complaining about being hurt by a petition written and signed by people you've hurt? Not classy.