The point here bears repeating: while lineage, or identity as a Jew, was once transmitted only from father to child, then only from mother to child, in our time the Reform and Reconstructionist movements have ruled that, given other required conditions such as a Jewish upbringing, Jewish identity can be conferred by either parent. This ruling is without question a radical but logical innovation of great magnitude and consequence.
At first this change – recognizing (again, as in biblical times) paternal descent as establishing Jewish identity - was put in effect and practiced in Reform synagogues unofficially. Theological justifications were not thought necessary. For decades, Reform Rabbis and their congregations would simply ignore maternity or paternity issues altogether once a child was enrolled in a synagogue’s religious school and the family made clear its decision to raise exclusively Jewish children.
The welcoming ceremony of Consecration for all children at the time of enrollment, documented in the annals and archives of a congregation (invariably Reform), sufficed to establish and authenticate Jewish identity regardless of which parent was Jewish. Jews, throughout their relatively lengthy history, have been less concerned with abstract principles than matters of conduct and ever-evolving behavioral norms - which realistically and humanely address new conditions and novel circumstances. These judicious and compassionate acts of inclusion preceded any theoretical justification or supporting theology of the sort being presented in this essay.
Consistent with this profound and fundamental innovative ruling by Reform and other Polydox movements that Jewish identity may now resolutely and validly be conveyed by either parent, women "gave up" sole possession of its transmission. It might be said that relinquishing their monopoly they advanced equality!