Did Christians stop the practice of Berith (Brith, Bris?) immediately and based on which scripture?
This was a topic of dispute in early Christianity, between believers who had come from the Jewish faith, and gentiles. The issue relates to whether Christianity is part of Judaism - which would mean that converts had to be circumcised - or whether it is an independent faith. If it is not needed for adult converts, then it would not be applicable for children either.
Acts 15:1-21 records a council, held in Jerusalem, to decide. This probably took place in 50 or 51AD. Peter said (v7-11, NIV):
and the council agreed to write to Gentile believers, saying (v28-29):
That did not entirely settle the issue, since it says nothing about whether Jewish converts could or should observe the law of Moses, and in addition there continued to be many "Judaizing" Christians that required converts to be circumcised and follow the Torah. Historically speaking, the destruction of the Temple in 70AD, and the Roman slaughter and dispersal of Jews, dramatically reduced their numbers and influence. Though groups such as the Ebionites continued to exist for several centuries after that, "mainstream" Christianity no longer required circumcision at all.
Paul writes about circumcision at great length in his letters, especially in Galatians but also in Romans, 1 Corinthians, and elsewhere. For example, Romans 2:25-29 says:
His theological case is that circumcision is a sign of faith, but it is not the same as actually having faith. For Paul, the outward symbol is unnecessary. More generally, one of his major themes is that adherence to the Law does not guarantee salvation (see Galatians 5, for example).