Blixa asked:

[is it] possible to tell a non-antisemitic "passion" story (by your standard), [and] how would one go about doing it?

Yes. Basically you follow the guidelines laid down by the Second Vatican Council, the rejection of which is the defining doctrine of Gibson's religion.

This question is on the Anti-Defamation League's FAQ on The Passion (the whole of which is worth reading – though I suppose not if you find it hateful, stupid, junk, and obscene). They say:

The story of the Passion can be told without disparaging the Jewish people. Such an account is mandated by the Catholic Church as a result of the Second Vatican Council, which in 1965 repudiated both the deicide charge and all forms of anti-Semitism in its document, Nostra Aetate. Most Protestant churches followed suit, and since 1965 Christians have worked cooperatively with Jews to correct anti-Semitic interpretations within Christian theology. Aside from theological considerations, artists have a moral and social responsibility to avoid promoting material that may foster hatred, bigotry and anti-Semitism.