Would a person with a Jewish mother be denied Israeli citizenship -- i.e., denied his or her Jewishness -- merely because he or she had come to believe that Jesus was the Messiah prophesied by Isaiah, Jeremiah and King David?
"Jew" has two meanings, an ethnic and a religious one. "Jews 4 Jesus" is a religious concept so it makes no sense to presume the ethnic meaning. Since they go to great lengths to assert that their beliefs fit within a Jewish theological framework, it would also contradict their own usage of the word to claim they're citing the ethnic usage.