Maggid Mishneh Hilkhot Ishut 4:15

From the sugya from the first chapter of Yevamot (16b), it seems to me that even the child born to a Jewish apostate can participate in Jewish marriage with another Jewish woman… and even if she is an apostate as well…

Sefer Ha-Ittur, kof – Kiddushin, 78a, R. Yitzhak b. Abba Mari, Marseille, 12 th c.

However, in the responsa of earlier authorities we find that one who violates Shabbat is no longer Israel, for it says, “between me and Israel”: anyone who keeps Shabbat is called Israel, and it is taught that one does not accept sacrifices from an apostate who is an idolater or who violates Shabbat in public. Therefore, one who violates Shabbat in public is a Gentile and is incapable of effecting kiddushin. But Gentiles today outside of the land of Israel are not idolators [this is based on a statement in Bavli Hullin 13b—EMT] so a contemporary [Jewish apostate] can’t possibly be classed as an apostate idolater. And the rule concerning public Shabbat violation only applies to those who work the land [and Jews are mostly not involved in agriculture—EMT]. Therefore, [contemporary apostates] effect valid Jewish marriage and divorce.

Rambam Responsum #293

…The core point is that Avraham our father is the one who taught and educated the people, informing them of the religious truth and the unity of God, rejecting idols and their worship. He brought many into the Divine Presence and taught, instructed and commanded his descendants to follow God’s way, as it is said in the Torah, “For I have singled him out, that he may instruct his children and his posterity to keep the way of the Lord…” Therefore, anyone in any generation who converts and anyone who unifies God’s name as is written in the Torah is a student of Avraham our father and a member of his household, and Avraham himself is responsible for setting him on the right path just as he did to the people of his own generation…Avraham our father is thus the father to all of his descendants who properly follow his example and also a father to all of his students and to any future convert…