I am not Jewish nor am I any kind of expert on Jewish history and rabbinic teaching so take this with a BIG grain of salt. Yet I have read that Judaism has not always been matrilineal. Some earlier sects of Judaism (eg, Karaite) are patrilineal. Prior to rabbinic Judaism (Mishnah, Talmud), some say biblical Judaism was patrilineal. For example, Jabob's sons born of Bilhah (Dan and Naphtali) and of Zilpah (Gad and Asher) are the patriarchs of four of the twelve tribes of Israel, and yet Bilhah and Zilpah were not descended from Abraham--is that not right? Likewise, the Asenath, the Egyptian daughter of Poti-phera priest of On, was the mother of Manasseh and Ephraim.
This article might be worth a read. (Expensive unless you can find it in a scholarly library)
This article might be worth a read. (Expensive unless you can find it in a scholarly library)