It seems that this question has two points. First, when Christians stopped to practice Jewish traditions. Second, when others stopped to think that they are a Jewish sect. Either part has a strict border.
Regarding the first part, I would assume that this is related to the destruction of the Temple when many Christians left Palestine. This event also caused significant changes in the Jewish community: many Temple related rituals disappeared. No other change was so significant. On the other hand, there are some attempts to go back to the Jewish tradition and practices, e.g. Adventists of the Seventh Day.
Regarding the second part, the limited understanding in the Roman empire was caused by the illegality. Thus, the most important date seems to be 313. On the other hand, there are still people in the modern era who thought Christians to be a Jewish sect:
Historically speaking, the Christian religion is nothing but a Jewish sect.... After the destruction of Judaism, the extinction of Christian slave morals must follow logically.... Ah, the God of the deserts, that crazed, stupid, vengeful Asiatic despot with his power to make laws! (Adolf Hitler)
In some sense, Christians are a Jewish sect, they have Jewish roots and Christianity was founded by a Jew. This fact is obvious from the the Biblical canon, as well as from liturgy.