Christianity, all the way through to the end of the book of Acts, was a sect of Judaism, not something separate and distinct:
WEB Acts 2:46 Day by day, continuing steadfastly with one accord in the temple ...47 praising God, and having favor with all the people.
Note that the Christians were meeting in a Jewish place, praising God alongside other Jews in this Jewish place, having favor with those Jews, who would not take kindly to having their religion maligned in any way.
Acts 3:1 Peter and John were going up into the temple at the hour of prayer, the ninth hour.
Note that these new Christians still went to Temple at the hour of prayer, like good Jews would do.
Acts 5:42 Every day, in the temple and at home, they never stopped teaching and preaching Jesus, the Christ.
The Christians were still Jews, meeting in the Jewish temple.
Acts 9:1-2 But Saul, still breathing threats and slaughter against the disciples of the Lord, went to the high priest, 2 and asked for letters from him to the synagogues of Damascus, that if he found any who were of the Way, whether men or women, he might bring them bound to Jerusalem.
Note that Saul expected to find Christians in the Jewish synagogues.
Acts 10:28 [Peter] said to them, “You yourselves know how it is an unlawful thing for a man who is a Jew to join himself or come to one of another nation, but God has shown me that I shouldn’t call any man unholy or unclean. 29 Therefore also I came without complaint when I was sent for. I ask therefore, why did you send for me?”
Note that until the apostle Peter was given a special miraculous vision, he wasn't going to have anything to do with Gentiles.
Acts 10:34 Peter opened his mouth and said, “Truly I perceive that God doesn’t show favoritism; 35 but in every nation he who fears him and works righteousness is acceptable to him. 36 The word which he sent to the children of Israel, preaching good news of peace by Jesus Christ—he is Lord of all....
Note that up until this point in time, Peter was convinced that the message of Jesus was sent only to the children of Israel, and is astounded to realize that it's for non-Jews also.
Acts 11:1 Now the apostles and the brothers who were in Judea heard that the Gentiles had also received the word of God. 2 When Peter had come up to Jerusalem, those who were of the circumcision contended with him, 3 saying, “You went in to uncircumcised men, and ate with them!”
Note that the other apostles and Christians were shocked that Peter went to non-Jews.
Acts 11:18 When they heard these things, they held their peace, and glorified God, saying, “Then God has also granted to the Gentiles repentance to life!”
Note that the other apostles and Christians were finally convinced that Christianity was not just for Jews.
Acts 11:19 They therefore who were scattered abroad by the oppression that arose about Stephen traveled as far as Phoenicia, Cyprus, and Antioch, speaking the word to no one except to Jews only.
And yet some of them just couldn't get beyond the belief that Christianity was for Jews only.
Acts 11:25 Barnabas went out to Tarsus to look for Saul. 26 When he had found him, he brought him to Antioch. For a whole year they were gathered together with the assembly, and taught many people. The disciples were first called Christians in Antioch.
Note that it wasn't until non-Jews became followers of the Way that a new name was needed to refer to this non-Jewish branch of the sect.
Acts 13:2 As they served the Lord and fasted, the Holy Spirit said, “Separate Barnabas and Saul for me, for the work to which I have called them.” 3 Then, when they had fasted and prayed and laid their hands on them, they sent them away. 4 So, being sent out by the Holy Spirit, they went down to Seleucia. From there they sailed to Cyprus. 5 When they were at Salamis, they proclaimed the word of God in the Jewish synagogues.
Note that still, for the most part, Christianity was a Jewish phenomenon; the apostles didn't go to the Greek temples to preach, but to the Jewish meeting houses.
Acts 13:23 From this man’s offspring, God has brought salvation to Israel according to his promise, 24 before his coming, when John had first preached the baptism of repentance to Israel. 25 As John was fulfilling his course, he said, ‘What do you suppose that I am? I am not he. But behold, one comes after me the sandals of whose feet I am not worthy to untie.’ 26 Brothers, children of the stock of Abraham, and those among you who fear God, the word of this salvation is sent out to you.
Note that even though Paul was specifically called to be an apostle to the Gentiles, he still preached in his early years "to Israel", that the salvation was "for Israel", to the children of the stock of Abraham.
Acts 13:46 Paul and Barnabas spoke out boldly, and said, “It was necessary that God’s word should be spoken to you first. Since indeed you thrust it from you, and judge yourselves unworthy of eternal life, behold, we turn to the Gentiles. 47 For so has the Lord commanded us, saying, ‘I have set you as a light for the Gentiles, that you should bring salvation to the uttermost parts of the earth.’”
Note that finally Paul starts to get it; Christianity is not just for the Jews!
Acts 15:1 Some men came down from Judea and taught the brothers, “Unless you are circumcised after the custom of Moses, you can’t be saved.” 2 Therefore when Paul and Barnabas had no small discord and discussion with them, they appointed Paul and Barnabas, and some others of them, to go up to Jerusalem to the apostles and elders about this question.
Now Paul has to go back to the other apostles to convince them that the new Gentile believers don't have to "become Jews" to be included in the Way.
Acts 15:30 So, when they were sent off, they came to Antioch. Having gathered the multitude together, they delivered the letter. 31 When they had read it, they rejoiced over the encouragement.
Yea, the Gentiles don't have to become Jews to be saved!
Acts 16:4 As they went on their way through the cities, they delivered the decrees to them to keep which had been ordained by the apostles and elders who were at Jerusalem.
Let's tell all the Gentiles they don't have to become Jews!
Acts 17:22 Paul stood in the middle of the Areopagus, and said, “You men of Athens, I perceive that you are very religious in all things.
Now Paul goes to the Greek temples to preach.
Acts 18:7 He departed there, and went into the house of a certain man named Justus, one who worshiped God, whose house was next door to the synagogue. 8 Crispus, the ruler of the synagogue, believed in the Lord with all his house. Many of the Corinthians, when they heard, believed and were baptized.
But Paul still does most of his preaching to the Jews, sometimes converting the ruler of the synagogue.
Acts 18:17 Then all the Greeks laid hold on Sosthenes, the ruler of the synagogue, and beat him before the judgment seat. Gallio didn’t care about any of these things.
Sometimes these converted synagogue rulers retained their position as synagogue ruler. (This particular one winds up co-writing 1 Corinthians - 1 Cor 1:1.)
Acts 18:26 He began to speak boldly in the synagogue. But when Priscilla and Aquila heard him, they took him aside, and explained to him the way of God more accurately.
Note that Priscilla and Aquila are still assembling in the synagogue. Cf the Greek of James 2:2, which also shows Christians meeting in synagogues.
Acts 21:21 They have been informed about you, that you teach all the Jews who are among the Gentiles to forsake Moses, telling them not to circumcise their children neither to walk after the customs. 22 What then? The assembly must certainly meet, for they will hear that you have come. 23 Therefore do what we tell you. We have four men who have taken a vow. 24 Take them, and purify yourself with them, and pay their expenses for them, that they may shave their heads. Then all will know that there is no truth in the things that they have been informed about you, but that you yourself also walk keeping the law.
The rumor was that Paul was telling Jews to stop being Jewish; that was a false rumor. In fact, Paul himself continued being Jewish, walking according to the Law of Moses.
Acts 23:6 But when Paul perceived that the one part were Sadducees and the other Pharisees, he cried out in the council, “Men and brothers, I am a Pharisee, a son of Pharisees. Concerning the hope and resurrection of the dead I am being judged!”
Paul declares himself, loudly, to be a Pharisee, currently. Not a former Pharisee. He's still very much a Jew.
Acts 24:5 For we have found this man to be a plague, an instigator of insurrections among all the Jews throughout the world, and a ringleader of the sect of the Nazarenes.
Note that the enemies of Paul considered his new religion a "sect" aimed at Jews.
Note that the enemies of Paul considered his new religion a "sect".Acts 24:14 But this I confess to you, that after the Way, which they call a sect, so I serve the God of our fathers, believing all things which are according to the law, and which are written in the prophets;
Acts 25:8 while he said in his defense, “Neither against the law of the Jews, nor against the temple, nor against Caesar, have I sinned at all.”
Paul has done nothing against the Jewish law or temple.
Acts 25:18 Concerning whom, when the accusers stood up, they brought no charge of such things as I supposed; 19 but had certain questions against him about their own religion, and about one Jesus, who was dead, whom Paul affirmed to be alive.
Note that Governor Festus believed Christianity to be about "their own religion", referring to Judaism.
Acts 26:3 especially because you are expert in all customs and questions which are among the Jews.
Note that Paul's defense hinges on the customs and questions among the Jews.
Acts 28:7 After three days Paul called together those who were the leaders of the Jews. When they had come together, he said to them, “I, brothers, though I had done nothing against the people, or the customs of our fathers, still was delivered prisoner from Jerusalem into the hands of the Romans....
Note that Paul had done nothing against Judaism.
Acts 28:22 But we desire to hear from you what you think. For, as concerning this sect, it is known to us that everywhere it is spoken against.
Note that in context, the Jews in Rome had not gotten any letters or info from Judea against Paul, only against his sect.