We have to distinguish between biblical law and rabbinic law. During biblical times a foreign wife moved into the Israelite husband’s clan and assimilated into it. Conversion for her was an impossibility. The woman could never became an Israelite, but the children produced by this marriage were Israelites. A change happened during the Talmudic period. Ethnicity and religion separated making conversion for the first time a possibility. For first time a foreigner can join the Jewish people. Today’s daf TB Yevamot 23 is a source of matrilineal descent. The mother confers the Jewish or Gentile identity to her child.

“Rabbi Yoḥanan said in the name of Rabbi Shimon ben Yoḥai: The verse states: “Neither shall you make marriages with them: Your daughter you shall not give unto his son, nor his daughter shall you take unto your son, for he will turn away your son from following Me” (Deuteronomy 7:3–4). This teaches that your son born from a Jewish woman is called your son, but your son born from a gentile woman is not called your son, but her son. The verse teaches that since the son of a gentile woman is her son alone, he is not considered related at all to his Jewish father.” (Sefaria.org translation)

The classic definition of who is a Jew is a person who is born to a Jewish mother or converts. The conversion is a two-step process. The convert studies Judaism for a period of time under the guidance of a rabbi. When successfully completing the course of study, the convert immerses into the mikvah And if he is a male, he also under goes circumcision or having already been circumcised he undergoes a symbolic ceremony called hatafat dam brit. A Jewish court of three certifies that both steps have been successfully completed according to Jewish law.

The Conservative movement has made this two-step process of conversion a standard. This means that there is no dissent and anybody who violates the standard can no longer be a member of the Rabbinical Assembly and enjoy all rights and privileges of membership in this body of Conservative rabbis.

In 1983 the Reform movement wrote a teshuvah legitimizing patrilineal descent. With caveats either the father or the mother can pass down a Jewish identity. In part their teshuva reads: “The resolution goes on to enumerate some of those public and formal acts which might serve to confirm what it terms the child’s “positive and exclusive Jewish identity.” Among these are religious study and participation in a ceremony of Bar or Bat Mitzvah.

“One might possibly assume that this young man qualifies as a Jew under the resolution, since he has attended religious school and observed his Bar Mitzvah in the synagogue. This assumption, however, is erroneous. The point of the Resolution on Patrilineal Descent, as it has been interpreted by this Committee and through the accumulated practice of Reform congregations, is that Jewish status is not automatically conferred upon the child of one Jewish and one non-Jewish parent. The child’s Jewishness is a “presumption” which must be established through a pattern of behavior which testifies to the desire of the parent(s) to raise the child exclusively as a Jew. Therefore, the “public and formal acts” of which the resolution speaks can confirm a child’s Jewishness only to the extent that they offer proof that such is indeed the intention of the parent(s).These actions must serve as “meaningful acts of identification” with the Jewish faith and people. As we have written:

“These acts of Jewish identification, though “public” and “formal,” are more than mere public formalities. To be “meaningful,” they must offer evidence that the child in fact identifies as a Jew and that the parents are willing and able to transmit a sense of Jewishness to their son or daughter. If they offer no such evidence, then they become meaningless, mere words and empty ceremony that tell us nothing of the depth of a child’s identification or of the parents’ capacity or sincerity in fulfilling their promise to raise the child as a Jew.” (https://www.ccarnet.org/responsa-topics/on-patrilineal-descent/fifth)

Was this change good for the Jews? In 2013 the Jewish People Policy Institute studied the impact of patrilineal descent. This is a synopsis of what they discovered:

“Patrilineal Descent in American Reform Judaism

5/06/2013

The American Jewish Reform movement’s 1983 Patrilineal Descent decision declaring that the children of Jewish fathers have the same Jewish status as the children of Jewish mothers affected all of American Judaism, because more American Jews call themselves Reform than any other wing of Judaism.

Many advocates, including the influential Rabbi Alexander Schindler, celebrated the decision as promoting “the full equality of men and women in religious life.” However, Sylvia Barack Fishman’s in-depth study of the sociological results of the Patrilineal Descent decision over the past 30 years reveals many unintended consequences.

Patrlineal Descent accelerates declining numbers of mothers in Jewish families who identify as Jews, increasing Patrilineal Jewish families with Jewish fathers who are among the least Jewishly connected Jews in America today. The study documents the differences between inmarried, Patrilineal, and Matrilineal Jewish families and offers policy suggestions based on that research.” (https://jppi.org.il/en/article/english-patrilineal-descent-in-american-reform-judaism)