At what point did Judaism and Christianity diverge? At what point did Judaism and Christianity diverge? Christianity and Judaism share the Old Testament (The Hebrew Bible), so it should be safe to assume they are the same people at least during the Old Testament period. Since when did they disagree?
tl;dr&gt; It began in the Council of Jersualem (55 AD), but was cemented by the destruction of the Temple in 70AD.

1. Gentiles were released from Jewish custom
The divergence is clearly articulated in Acts 15 - at the &quot;Council of Jerusalem,&quot; often pegged at 50 AD - roughly 20 years after the Crucifixion.  Acts 15 sets up the situation as follows:

Certain people came down from Judea to Antioch and were teaching the believers: “Unless you are circumcised, according to the custom taught by Moses, you cannot be saved.” 2 This brought Paul and Barnabas into sharp dispute and debate with them. So Paul and Barnabas were appointed, along with some other believers, to go up to Jerusalem to see the apostles and elders about this question. ... Then some of the believers who belonged to the party of the Pharisees stood up and said, “The Gentiles must be circumcised and required to keep the law of Moses.”

In a nutshell - it's the old circumcision debate: Do converts need to go under the knife?
Prior to this disagreement, Christians were simply Jews that believed Jesus was the promised Messiah.  When the Messiah came, however, he expanded His mission in such a way as to afford salvation to the Gentiles.  (See Matthew 28:19-20)
Peter speaks to this issue, recalling the fact that the Gentiles were being added to the mission - first in Acts 10, and now again in Acts 15:

6 The apostles and elders met to consider this question. 7 After much discussion, Peter got up and addressed them: “Brothers, you know that some time ago God made a choice among you that the Gentiles might hear from my lips the message of the gospel and believe. 8 God, who knows the heart, showed that he accepted them by giving the Holy Spirit to them, just as he did to us.

That they were included, however, necessarily raised the question of whether or not converts needed to follow all the practices of the Jews.  Peter, Paul, Barnabas, and the other apostles were clear that the grace of God implied that Gentiles need not do Jewish custom.

“It is my judgment, therefore, that we should not make it difficult for the Gentiles who are turning to God.

It was even suggested that a letter should be written, in which they said:

Therefore we are sending Judas and Silas to confirm by word of mouth what we are writing. 28 It seemed good to the Holy Spirit and to us not to burden you with anything beyond the following requirements: 29 You are to abstain from food sacrificed to idols, from blood, from the meat of strangled animals and from sexual immorality. You will do well to avoid these things.

By exempting the Gentiles from the rest of Jewish practice, a separate identity began to form.
2. The Persecution of the Jews diminished their importance in the Church, and vice versa
With the destruction of the Temple 15 years later, it simply became much harder to become a Jew.  As OzTorah writes:

In the post-destruction Jewish community, re-grouping and greater solidarity moved the Judeo-Christian group to the fringes. The earlier latitude towards separatist and fringe groups had become a luxury, especially when the Jesus party increasingly distanced themselves from their fellow Jews. The Judeo-Christians suffered a diminution in numbers and now, though not without an internal struggle, rebuilt and repositioned themselves as an increasingly gentile group, with new adherents directly coming to the new group without having to go through the old one first. They were not a monolithic community; they included at least four sub-groups (Ebionites A, Ebionites B, Nazarenes, Gnostic Sycretists and Elkesaites) – but they, like the Jews, needed to find sufficient unity to plan a secure future.
After much internal debate it became possible for an outsider to become a Christian without ever being part of Judaism, either through genealogy or choice. Could you be a Jew without the Sabbath, festivals, circumcision (Jews were not the only ancient people to view uncircumcision as shameful) and dietary laws? The answer was no – but you could become a Christian. Could you be a Jew without saying Sh’ma Yisra’el – “Hear, O Israel” and proclaiming the absolute invisibility and indivisibility of God? – again no: but you could become a Christian if you accepted the re-worked status of Jesus (developed and taught by Paul and his supporters though not necessarily required by a reading of Jesus’ own words) as messianic and part of divinity.
Sharper language than ever before began to be used in Judaism – it was a time of crisis when it was necessary to know where people stood – and heretics could no longer be treated with kid gloves. About the end of the century the Synagogue liturgy introduced a prayer which came to be known as Birkat HaMinim, the Blessing (Against) the Sectarians. ...
There was no authoritative decision to expel the Christians from Judaism but their exclusion came about gradually. The gentile Christians never were part of Judaism. The Jewish Christians still met halachic (Jewish legal) identity criteria but were excluded from officiating at Jewish worship because they regarded Birkat HaMinim as directed against them – whatever its motives at the time of its formulation – and their books were deemed to lack sanctity. In consequence they felt increasingly unwelcome. Christians were still found in the synagogues at least until the time of Jerome in the fifth century CE. In the second century CE Justin Martyr agreed that Jewish Christians who continued to follow Jewish usages were still to be considered “brethren” but as time went on, pressure was exerted to discourage the practice of Judaism by Christians.
The final break was due to the Romans when Jews (including Jewish Christians) were prohibited from entering Jerusalem; the re-established Jerusalem Church was thus an essentially gentile one.

With this polarization, rapid growth outside of Israel (Paul's ministry, in particular, was centered in Turkey and Greece, as evidenced by the fact that Corinth, Galatia, Ephesus, Phillippi, Colossae, and Thessaly all got their own books of the Bible!), and the persecution of the Jews inside of Israel, led to an imbalance of population.
Basically, the &quot;Jews&quot; dwindled and the &quot;Gentiles&quot; grew.  That, coupled with the freedom from the practices of the Jews eventually led to a situation where the church's early identity divested itself of its Jewishness.
3. By the second century, there was hostility
With the firm acceptance of Paul's letters by the end of the first, the anti-Judaizer faction became well entrenched.  By the middle of the second Century, some heretics like Marcion were already trying to remove any vestigial Jewish influence. When Marcion produced his first canonical list, for example, the entire Old Testament was relegated to non-canonical status. (Note - Marcionism is considered heretical nowadays, and rejecting the Old Testament is considered heretical, but I point it as way of evidence that the split had already occurred.)
By this time, &quot;Christ-killer&quot; rhetoric and the like, along with regional chauvinism prevailed, and enmity between the Jews and the Christians was mainstream. Modern Judaism took root in the Pharisitcal and Essene movements and followed its own course thereafter.