I can certainly speculate if you like.
I'm convinced their messiah will be Jewish, partially Jewish, or at least have credible evidence that he is.
I think we need to look at this in light of what happened right after Jesus' Ascension, where SOME Jews, namely Pharisees and Sadducees persecuted and killed other JEWS, who had accepted their Messiah, and spread His Gospel. We must remember that we have been grafted in to THEM, the True Jews, not the other way around. Obviously I am NOT suggesting we need to follow Jewish Law.
I think a similar scenario will shape up at that time. You will have those CLAIMING to be Jews, but are of the synagogue of satan, persecuting and killing not only other Jews, but Christians as well.