The first issue is that the compositional date for the Gospel of Matthew is a complex concept, because it was compiled from two major traditions, the first being the Gospel of Mark and the second a source normally referred to by scholars as "Q". Both of these sources themselves trace back to oral traditions about the life of Jesus and were gradually edited into the form we have now.
The single most important event affecting Jewish Christianity and Judaism in this period was the destruction of the Jewish Temple in Jerusalem by Titus in 70 AD. Because much of Jewish ritual law centered around the Temple, this hastened the decline of observance of Jewish purity laws by Christians (and the disappearance of observant Gentiles) and the end of Jewish Christianity. The destruction of the Temple can be said to be a crucial factor in the triumph of Pauline or Gentile Christianity within the Christian Church.