Lawrence Schiffman discusses the subject in an essay here.
The split between Judaism and Christianity did not come about simply or quickly. It was a complex process which took some one hundred years, starting from the crucifixion, and which had different causes and effects depending on whether it is looked at from the point of view of Judaism or Christianity. Further, the question of legal status as seen through Roman eyes also had some relationship to the issue.
And then the rest (from a publication of 1991 which is nevertheless still interesting).