Checklists & THE IMPERIAL RELIGION (DB) The checklist approach to making an absolute divide between Christian & non-Christian, between Jew & non-Jew, came into it's own under the Christian Roman Empire, which set much store in getting all the messiness sorted out.
For many years it was believed that an early period of fluidity came to an end in a definitive "parting of the ways" that took place in either the first or second century.
The argument was twofold. On one hand, the Temple had been such a unifying force that other forms of diversity were much more tolerable without threatening the core of Jewish identity. Following the destruction of the Jerusalem Temple by the Romans in A.D. 70, other ways had to be produced to secure such identity, hence the invention of a Jewish orthodoxy that ex-cluded followers of Ye(ho)shu(a) (haNatsri aka haMashiah etc.).
On the other hand, we are told that it was the divergence of Christianity from that core that drove an early parting pf the ways. I (DB) contend that such diversity did not end with the destruction of the Temple and continued well beyond this event.
Many have thought until recently (& some still do) that it ended with the Council of Yavneh, which allegedly took place in A.D. 90 or so. According to a certain interpretation of the Talmudic Legend, this was a great Jewish ecumenical council (something like the great Christian ecumenical councils of the fourth & fifth centuries) in which all sectarian differences were abolished: all Jews agreed to follow the pharisaic-rabbinic tradition, & those who didn't were expelled & left the Jewish polity.
But this view has largely been discredited by recent scholarship. It was invented by scholars more or less on the model of the great late-ancient Christian councils during which Christian orthodoxy was promulgated, especially the famous Council of Nicaea & it's successor the Council of Constantinople. In 381 at Constantinople the definitive step in cleaning up the differences based on a half century of negotiations following the Council of Nicaea was taken.
In 318 the newly Christian emperor Constantine had called an ecumenical council of bishops from all over the Christian world to come to Nicaea (present-day Iznik in Turkey) to sort all of this put & restore peace to the Christian churches & communities, following a great deal of dissension, conflict, & bitterness between them.
Some of the major issues addressed @ Nicaea were matters of creed, such as the precise definition of the relationship between the Father & the Son. Others were matters of practice, such as the correct date of Easter & the relationship to the Jewish Passover.
It was here, @ Nicaea, that on the first question it was decided that the Son was consubstantial with the Father, that is, they are two persons of the exact same divine substance. Easter was severed once & for all within orthodox churches from its calendrical & thematic connections with Passover. In the end what was accomplished in Nicaea & Constantinople was the establishment of a Christianity that was completely separated from Judaism.
Since Christianity could not define it's borders on the basis of ethnicity, geographical location, or even birth, finding clear ways to separate itself from Judaism was very urgent ~ and these councils pursued this end vigorously.
This had the secondary historical effect of putting the power of the Roman Empire & its church authorities behind the existence of a fully separate "orthodox" Judaism as well. At least from a juridical standpoint, then, Judaism & Christianity became completely separate religions in the fourth century. Before that, no one (except G d, of course) had the authority to tell folks that they were or were not Jewish or Christian, & many had chosen to be both.
At the time of Yeshu ("Jesus"

, all who followed Yeshua - & even those who believed that he was G d - were Jews!