Were the Avos Jewish?

The Parashas Derachim is famous for the first two essays in the sefer which discuss whether ths Avos had the status of bnei noach or yisraelim before mattan torah. One of the mareh mekomos that seems to address this issue is found in this week’s parsha. A certain person who was “ben yisraelis v’hu ben ish mitzri” committed the cheit of being a “mekallel” and was punished for the offence. The Ramban cites the Chachmei Tzorfas who held that this person was in fact not Jewish – even though we pasken that a child of a Jewish mother is Jewish, this person joined Klal Yisrael before mattan Torah when lineage was based on the father’s identity. The Ramban takes issue with the Chachmei Tzorfas and writes that since the time of Avharam Avinu anyone who joined Klal Yisrael was granted Jewish identity based on his mother’s lineage. According to the analysis of the Parashas Derachim, the Rambam holds that even the Avos had the status of yisraelim, while the Chachmei Tzorfas disagree.
Rav Hershel Schachter in his sefer Eretz haTzvi takes a slightly different approach. R’ Shachter argues that lineage based on the father’s identity is a function of being subsumed in a family group – mishpachas av is called mishpacha, not mishpachas eim. We identify the child of a Jewish mother as a member of Klal Yisrael because of the unique din that the role of mishpacha is secondary and subsumed under the individual’s relationship to the nation of Klal Yisrael, which follows the mother’s identity. The machlokes Ramban and Chachmei Tzorfas is not whether Avraham had the status of a Yisrael, but whether that status of Yisrael which existed at the time of the Avos was based on the din of mishpacha or on the din of nationhood.