Can you provide a clear and cohesive explanation of what that meant to the Saducees, Shammai Pharisees, Hillel Pharisees, Essenes, Zealots, ascetics, mystics, tax collectors, priests, scribes, diaspora Jews and gentile converts of Jesus' day?
On the one hand, 1st century Judaism was diverse enough that it seems to me any would-be argument that "no true Jew" would claim or teach whatever is attributed to Jesus, Paul and so on are obviously and laughably fallacious (regardless how frequently variations on them may be raised even sometimes by serious scholars). On the other hand, it means that there's probably nothing in the NT that is really and radically new: Not the notion of justification through sincere repentance and faith rather than ritualistic sacrifice or good deeds, not the notion that the written Torah was an incomplete or otherwise limited source of divine guidance, not even the notion of a divine Logos as a sort of secondary god.
Even Jesus' commands to forsake all possessions - despite being quite different from a previous strand of Jewish (and probably all other cultures') propaganda suggesting that material wealth was a sign of divine favour - were preceded by the asceticism of folk like John the Baptist and perhaps influenced from outside the strictly Jewish tradition by the likes of Cynic philosophy.