In the past there have been Jewish movements accepting Jesus, Shabbatai Tzvi, and Menachem Schneersohn as Mashiach. These movements cease to be Jewish when they accept non-Jewish Mashiach as G-d theologies like that written in the "Gospel of John" and by the epistles of Paul of Tarsus (Romans, Galatians, Corinthians, etc). Those that deny the oral history of the Jews are not Jewish movements.
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from the article: Wave of vandalism hits non-Orthodox synagogues anew