I beg to differ. The ADL at this juncture means just one man: Abe Foxman. He saw an opportunity to scare some ignorant old Jewish people into giving him money. Foxman is a "show me the money" kind of guy and I doubt that he knows from a watered-down modern interpretation of the gospels one way or the other. Don't confuse Foxman with an ideological liberal or an ideological anything else. He is trading on the reputation of the old ADL of B'nai Brith to make money.
I'd say he's using Mel to generate funds, and doesn't mind giving Mel some free publicity in exchange. Not that Mel would ever see it that way. Foxman is a stinker and a hustler, but not a "typical liberal".
The Catholic bishop's group, on the other hand, dislike Mel over the issue of the Latin Mass and general political conservatism. I don't think that anything as deep as New Testament interpretation motivates them.
I haven't actually seen the movie yet, but doesn't it depict the Romans as carrying out the execution? I know this is what the New Testament says.
Was Jesus framed by the Sadducees who had commandeered the running of the Temple as the New Testament says? I'm not a Christian, so I don't believe that as a matter of faith. But it's possible given all the other evidence, and in any case no present day sect of Jews (or even Foxman) are Sadducees.