I've got kinda mixed feelings on this one. They're doing an impression, it seems to me like imitating any relevant speech impediments is gonna need to be part of that imitation. I don't see it as criticizing him for having a stutter, but just having fun with the vocal fingerprint it contributes to. Even if Alex Jones wasn't a complete piece of shit, I think they'd be having fun with the stutter all the same, because that's just part of how he talks and the joke is using "his" voice to say silly things.

It reminds me a bit of how people always imitate Obama saying "uh" a lot. Plenty of them love Obama, it just happens to be a marker that makes his speech stand out.