In short: It depends on your definition of the term: “Jewish”.
According to orthodox rabbis from organizations which operate: “Ask the rabbi” websites like A.I.S.H and the Chabad Movement, then the definition of: “Jewish” is those who were born Jewish and live a lifestyle according to the rabbinical “hahlacha” (i.e. the oral law ). In other words: Since Abraham, Isaac and Jacob did not live a lifestyle according to the rabbinical “hahlacha”; then they were not Jewish.
So, for example: Rabbinical law states that Judaism passes thru the mother (i.e. Judaism is based on matrilineal descent). Since Sarah is not the mother of Rebecca and Rebecca is certainly not the mother of Leah, Rachel, Bilhah and Zilpah; then, not only weren’t Abraham, Isaac and Jacob not Jewish, but NONE of the original 13 “Children of Israel” were Jewish either. (Actually, we do not even know the names of the mothers of Sarah, Rebecca, Leah or Rachel, much less the nationalities of Bilhah and Zilpah).
In fact, some rabbis go even further and claim that Abraham, Isaac and Jacob followed something they like to refer to as: “The Noahide Laws” or the laws that were given to Noah. This, of course, is ridiculous since Noah was never told to separate himself from his family and move to a land God would show him; nor was Noah ever commanded to circumcise his children. The only law we can assume that both Abraham and Noah shared was the commandment not to eat blood.
What we do know, however, is that God told Isaac that he would receive the land of Canaan as an inheritance because his father followed God’s ways and obeyed God’s laws. In the Book of Deuteronomy Moses says that the inheritance of Israel is God’s laws.
This issue of whether or not Judaism is based on matrilineal descent is not limited only to Abraham, Isaac and Jacob. We are clearly told that the first wife of King Solomon (i.e. the wisest Jew who ever lived) was an Egyptian. We are later told that because of his foreign wives, Solomon was led into a lifestyle of worshiping foreign Gods. This then raises the issue of: Who was the mother of Solomon’s son: King Rohobaum? According to Wikipedia: his mother was Naamah the Ammonite. Was Naamah the Ammonite Jewish ? Some rabbis say she was and that she converted to Judaism. Really? But: If Solomon’s wives converted to Judaism, why then did they convince him to worship foreign Gods? Furthermore, King Ahab was the father of two Kings of Israel and there is absolutely no way that the rabbis could argue that Jezebel converted to Judaism, since King Ahab built her a temple of Baal for a wedding present.
Some rabbis like to say: “Well, King Ahab wasn’t really Jewish….”. Okay fine, but where does it end ? Abraham, Isaac and Jacob weren’t really Jewish. King Ahab wasn’t really Jewish. Gentiles converted in the United States aren’t really Jewish. A large percentage of the Russians now living in Israel aren’t really Jewish.
In fact, according to the rabbinical definition of Judaism, the national hero: Joseph Trumpeldor; a man who was one of the founders of: “The Zion Mule Corp” in World War One and one of the fallen defenders of Kibbutz Tel Hai, was not Jewish (Not to mention: he was a man who has hundreds of streets in Israel named after him).
In conclusion, the Bible tells us that God spoke repeatedly with Abraham, Isaac and Jacob and that the sole reason the nation of Israel exists today is because of the covenant between God and these three men. Therefore, it would seem logical that the rabbis should stop worrying about whether or not Abraham, Isaac and Jacob lived according to the rabbinical oral laws and begin to worry whether they themselves live according to the laws God told Isaac he gave to Abraham….