You have not answered the question of whether a Jewish woman who leaves her religion, who is a reprobate and cosorts with Gentiles, who dies and is buried in a Christian cemetery is still a Jew. If she is, then ethnicity trumps religion, and that is what I’m trying to discern.
Even if he/she sinned, he is still part of Israel. Sanhedrin 43B is clear about that. The religion is latent in the soul of a non-believer, but is his/her birthright as a descendant of Israel, whether physically or spiritually through descending from converts, and that latent faith can and often is re-kindled unexpectedly. Not necessarily by reason of ethnicity, either. If one’s mother is Jewish by reason of her conversion to Judaism prior to one’s birth, that person is Jewish, be he ethnically Chinese, black, American Indian, Australian aborigine, or Martian. There are voluminous explanations as to why this is in books of Chassidic philosophy. I especially recommend the Tanya, Volume 1, Chapters 18 through 25, by Rabbi Shneur Zalman of Liadi, founder of the Chabad school of Chassidic Philosophy.