Yes, Jesus was Jewish. He was, in fact, so good at being Jewish that all the other Jews had to kill him to keep them from looking bad.
The understanding that he was killed by a select group of politically-motivated Jewish élite under the auspices of Imperial Rome, and NOT by an elective motion of the entire religion/culture is not easily explained to those with short attention spans. If you want a sociological primer for millions of deaths stemming from Anti-Semitic prejudice from roughly the 4th Century to the present, that's about it.
Oh, and Mel Brooks' whole "Gentiles can laugh at self-deprecating Jewish humor because we file their taxes for them anyways" shtick doesn't really help, either.