Also, CYE's humor is way beyond recitation of cliched stereotypes; common knowledge of stereotypes is the setup, not the punchline. Usually, Larry's elaborate mishaps while trying to escape, reverse, or disavow stereotypes creates the humor.
So perhaps if you now go through comically absurd lengths to prove both your religious sensitivity and your essential loyalty to The Tribe, but fail miserably so that by the end of the episode everyone is against you – then you can use the "I'm just like Larry David" defense.