In answer to “Rebbetzin Goldenpick…”:
1. Everyone knows that many baalei tseuvah aren’t Jewish (or more likely, aren’t sure they are Jewish). The line between “Baal Tseuvah” and potential Ger Tzedek will be increasingly fuzzy. The eventual solution will end up being to ask any (and all) Baalei Tseuvah to “convert” to resolve the safek. This is “old news” since among the non-orthodox Jews in the English-speaking countries who had been in their current homes since the mid-19th cenury, the process of assimimlation is already over 200 years old and these problems have been arising for some time. It was an issue among the pre-war (pre-quotas) East European immigrants by the late 20th century, and should now be an issue among post-World War II arrivals. Like it or not, most Jews have been non-frum since the 18th century, and non-frum Jews frequently marry goyim.
2. The majority opinion is that a non-Jewish wedding ceremony (presided over by a judge or a minister), or a common law marriage (whether or not recognized by the government), or a “Reform” wedding, when it is obvious the parties have no intention of being married according to Jewish law, does NOT create a Jewish marriage and therefore subsequent children that the woman has by some other man ARE NOT MAMZERIM. If you hold that two non-religious Jews “living together” constitutes a valid halachic marriage, then at this point in time most non-religious Jews are probably at least safek mamzerim, however it appears that most poskim do not hold this way but rather will invalidate a marriage based on such evidence as treff food at the wedding or the bride not going to mikva or hillus Shabbos (all indicative of lack of intent by the parties to be married “K’daas Moshe ve-Yisrael”).
3. Increasingly most non-Jews we encounter will have some Jewish ancestry. This reduces the chance of a Hitler-like persecution based on ancestry. It also raises a real shailoh about use of a Shabbos-goy or selling matza to a goy on Pesach.