From Acts 1-9 of the New Testament, in what ways did the earliest followers of Jesus continue to be part of the larger Jewish community?
One of the key points in understanding the early Christians is to realize that they did not see themselves as a separate religion from Judaism. Christianity is Messianic Judaism, the belief that Yeshua ben Joseph was the fulfillment of the teachings of Moses and the Prophets. We see in these chapters the early proto-church worshipping at the Temple, following the Jewish customs and celebrating the Jewish holy days the same as other Jews. In chapter two we see them in the midst of Shavuot, the Festival of Weeks, which is referred to as Pentecost in the New Testament. In chapter three Peter and John go to the Temple, etc. The explanation of the Pentecost and Peter's defense of the miracle at the Temple are constructed on the foundation of Jewish history and the religious beliefs of that culture. The teachings and life of Jesus (Yeshua) are presented in the light of the history, culture and religion of the Jewish people. Peter traces the history of the Hebrew people and their teachings from the earliest point up to the life, death and resurrection of Yeshua as an unbroken narrative.
Interestingly, the point at which non-Jews become truly accepted among these early Messianic Jews is in chapter ten, when the centurion Cornelius sends for Peter. "Centurion" is a less than perfect translation of his title, as it implies he was merely one of the officers of the Roman army in Palestine. He was the military commander of the Roman legion in Palestine, immediately under the Roman governor. There is mention of Gentiles believing in the God of Abraham before this, and in "Greek" believers in the Messiah in chapter six of Acts, but this is the point at which Gentiles become completely accepted by Peter and the other apostles.
Earlier, in the Gospel of John, the author of that book speaks somewhat harshly of "the Jews", but that author was of course himself Jewish. What he meant was the ultra-religious and powerful Jews, ie the Pharisees. It was they who put tradition above the scriptures, had Christ crucified and eventually drove many of the Messianic Jews away from Jerusalem. An interesting point about the dangers of publicly "religious" people with political power.