Rabbi Moshe Feinstein states the very marriage of a gentile woman to a non observant Jew, is equivalent to an open declaration that she will not observe the precepts. This is so, because it is highly unlikely that the gentile member of such a union, will be more committed to Judaism than her remiss Jewish husband (certainly when they are living together prior to their marriage and throughout the "conversion" process.) Unlike mental or tacit negations, explains Rav Feinstein, open declarations do invalidate conversions. When such cases appear before a rabbinical court, its members actually become witnesses to an acceptance declaration that is not sincere. Therefore, it is no longer a tacit insincerity, but rather an obvious one. (As such, they are forbidden to sanction the conversion. ) (Regardless of what this Jewish court may declare,) the conversion is invalid and the person is not deemed a member of the Jewish nation - not l'chatchila and not b'dieved (NEVER). In Iggros Moshe, Letters of Moshe (Yoreh De’ah, no. 157), he writes that “According to the Law, it is certain that one who converts for the sake of marriage, does not intend to keep the commandments, and is not a proselyte at all.” "It is beyond my comprehension why any (legitimate) rabbi would want to include such people amongst the Jewish nation."
(Language simplified and clarified for the vast majority of idiots among us)
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אגרות משה - חלק ב - פיינשטיין, משה בן דוד, 1895-1986 (page 1 of 554)