No, we're not, because I am not.
> whether his posting that video should be considered wrong
Consider it wrong, if you wish, and act accordingly. I don't consider it wrong, and I'm acting accordingly. Therefore, the question of appropriate consequences is not one I'd pay any attention to.
> ie parody should be excluded from ethical analysis
I don't know about shoulds, but so far, I haven't come across any parody that has gotten me all worked up. Let me lay out a few issues: when it comes to abortions, I'm completely pro-choice, and yet, I haven't come across any parodies made by pro-life people that has gotten me worked up. When it comes to human-caused climate change, I believe there is sufficient evidence for it, and yet, I haven't come across any parodies by those who deny it that has gotten me worked up. I'm an Indian, and I have seen plenty of cartoons and skits that parodies Indians, and yet, I haven't come across any that has gotten me worked up.
> Should they be automatically immune from societal rebuke?
I refuse to think on "society"'s behalf, and I'd definitely get worked up if someone claims to think on my behalf. If we are talking about violent activities, or activities that cause large-scale environmental damage [2], I'd participate in a discussion on how society should deal with it.
> we do not need to make any tortuous suppositions about the ethnicity of Muslims in the parody
All I saw was a caricatured generic Maulvi-type person, who could as easily have been British as Turkish, Arabic, Persian, Pakistani, Indian or Indonesian. I know that in the US, Arabs and Persians are considered "white". When there was a wide-spread scandal of the Catholic Church and sexual abuse of children, I did not concern myself with the issue of the ethnicity or the nationality of priests depicted in caricatures.
[2] - Edit: or fraud