Blubluh, I don’t think you’re correct about the standards of the Chief Rabbinate. My daughter is adopted. Her birth mother was Jewish. It was easier for her to get married in Israel (which needed the approval of the Chief Rabbinate) than to convince the medina she was Jewish for purposes of aliyah.
Joseph, Mormons don’t think they’re Jewish, but they call non-Mormons gentiles. So if you go to Utah, you too can be a gentile.