The question you are asking is often called "The Parting of the Ways" in scholarship, it is quite a debated topic. Generally it depends upon the scholars perspective on 1st century Judaism.

However, there is reasonably consensus that it was a process, and some of it's major factors were as follows:

• Sometime in the 50s AD, the so-called "Jerusalem Council" (Acts 15) agreed that Gentile believers did not have to follow the Mosaic Law as a whole.
• Paul's Letter to the Galatians, often dated to the early 50s, shows a clear debate within the Christian community over whether Law-observance is required of believers, especially those of a Gentile background.
• In the 60s AD, Nero at Rome blames the Great Fire on Christians, which can only occur with a clear idea that 'Christians' are an identifiable group
• The destruction of the temple and razing of Jerusalem in 70AD fundamentally alters Judaism. From this period only Christianity and Rabbinic Judaism emerge as continuing Jewish sects.
• The rapid growth of Gentile-constituents of the Christian movement, and the loss of distinctive Jewish identity

For my part, I would say circa 70 AD. But it's a process by which a Jewish sect that includes Gentiles becomes a distinct group that differentiates from 'Jews'. Before 70, I would say the lines are more 'blurry', but I think it's arguable they become much clearer from then on.