Here is a bit of perspective on the history leading up to the regional synod of Laodicea.
The Jewish believers in Jerusalem continued to observe the law, meet in Synagogues until they were kicked out, etc. When Saul wanted to arrest Christians in Damascus, before his conversion, He planned on going to the synagogues:
Act 9:1 But Saul, still breathing threats and murder against the disciples of the Lord, went to the high priest
Act 9:2 and asked him for letters to the synagogues at Damascus, so that if he found any belonging to the Way, men or women, he might bring them bound to Jerusalem.
Act 22:19 And I said, 'Lord, they themselves know that in one synagogue after another I imprisoned and beat those who believed in you.
This made sense because the Scriptures were read in the synagogue. Not everyone had scrolls. Eventually they were put out of the synagogues. We see this at times in Acts. Then they would meet in homes, or in one mentioned instance, a lecture hall daily.
James, during the discussion of Acts 15 regarding salvation by faith and circumcision, the law of Moses etc. makes reference to the continuing preaching of Moses in the synagogue and assumes familiarity with the practice on the part of all present, from the various churches throughout the world:
Act 15:21 For from ancient generations Moses has had in every city those who proclaim him, for he is read every Sabbath in the synagogues."
James references the synagogue when speaking to Jewish Christians:
Jam 2:2 For if a man wearing a gold ring and fine clothing comes into your assembly, and a poor man in shabby clothing also comes in,
Jam 2:3 and if you pay attention to the one who wears the fine clothing and say, "You sit here in a good place," while you say to the poor man, "You stand over there," or, "Sit down at my feet,"
Jam 2:4 have you not then made distinctions among yourselves and become judges with evil thoughts?
The word translated "assembly" here is the term for the synagogue.
James and the believers in Jerusalem were "zealous" for the law. Indeed, the Jewish believers there continued to practice the law and the traditions of the fathers and even Paul did so:
They note the distinction made at the Jerusalem council, recorded in Acts 15. The Jewish believers went on observing the law. But the Gentiles were under the mandate from the council.
Paul was being accused of turning away Jews in the diaspora from the law. In actuality Paul was upholding that Gentiles did not need to be circumcised to be in Christ.
But it shows that the Jewish believers continued with all the law, including vows, sacrifices, etc. The question in Acts 15 was not what the Jews should give up, but what should be required of the gentiles.
And this made sense because witnessing the Jews while throwing out the Torah wouldn't get very far.
In the same way Christian evangelism would be limited by requiring Gentiles to be circumcised and obey the entire law of Moses, which was not needed for them to receive Christ by faith. You can check out Galatians which touches on these issues thoroughly. Galatians also points out that Gentiles are not without moral requirements, and walking in the Spirit fulfills the law. in fact Paul would at times use specific OT commandments, including from the Ten Commandments, to teach moral principles.
Both groups recognized the Grace of Christ, and extended fellowship. For instance in Acts 21 James and the elders welcomed with joy the report of the evangelizing of the Gentiles.
The Jewish believers, who were the dominant force in the church until at least 70 AD, and likely continued to be at least partly until the total destruction of Jerusalem and conversion of it to a hellenistic city, were fully accepted as members of Christ, though keeping the whole law. Not only were they accepted ,but they were the norm. For the first years of Christianity the church had not fully understood Jesus' command to go to the Gentiles. You can Read Acts 10-11 for the background on that, and Acts 15.
With the destruction of Jerusalem in AD 70 the Jewish believers fled. But some continued that kept the law, and worshiped Christ. However, they grew apart from the gentile believers who now became the norm.
We see historical records of the "Nazarenes" who were Jewish believers.
Epiphanius' Panarionis a work that deals with all the heresies that the author is aware of. He resided in Palestine, so was closer to some of the issues in this regard. In this work he describes the Nazarenes:
For they use not only the New Testament but also the Old, like the Jews. For the Legislation and the Prophets and the Scriptures, which are called the Bible by the Jews, are not rejected by them as they are by those mentioned above [Manicheans, Marcionites, Gnostics]. Panarion 7.2
"Only in this respect they differ from the Jews and Christians: with the Jews they do not agree because of their belief in Christ, with the Christians because they are trained in the Law, in circumcision, the Sabbath, and the other things." "By birth they are Jews and they dedicate themselves to the Law and submit to circumcision." Panarion 7.5
However, they are very much hated by the Jews. For not only the Jewish children cherish hate against them but the people also stand up in the morning, at noon, and in the evening, three times a day and they pronounce curses and maledictions over them when they say their prayers in the synagogues. Three times a day they say: 'May God curse the Nazarenes.' For they are more hostile against them because they proclaim as Jews that Jesus is the Christ Panarion 9.2-3
"They have a good mastery of the Hebrew language. For the entire Law and the Prophets and what is called the Scriptures, I mention the poetical books, Kings, Chronicles and Ester and all the others, are read by them in Hebrew as in the case with the Jews, of course." Panarion 7.4
"They have the entire Gospel of Matthew in Hebrew. It is carefully preserved by them in Hebrew letters." Panarion 9.4
Jerome also references the Nazarenes who kept the whole law:
"The Nazarenes, who accept Christ in such a way that they do not cease to observe the old law, explain the two houses as the two families, viz. Of Shammai and Hillel, from whom originated the Scribes and the Pharisees." Jerome's Commentary on Isaih (on Isaiah 8.14)
Now here is the upshot. These believers were in most ways quite orthodox, with Jerome and Epiphanius giving indications that they were also orthodox in their Christology. However, Epiphanius considers them heretics because of their observance of the law.
But they are practically no different than James and his group of Jewish believers in Jerusalem. It appears over time the Jewish believers in Christ and the gentiles grew apart.
Another statement on this point is seen in Justin Martyr's dialogue with Trypho (a non-Christian Jew). This is an earlier date than Epiphanius actually, and we see the divide starting to happen. Justin makes reference to a group who believes in Christ, but keeps the Jewish law. He extends fellowship to them, but considers them weak-minded.
But if some, through weak-mindedness, wish to observe such institutions as were given by Moses, from which they expect some virtue, but which we believe were appointed by reason of the hardness of the people's hearts, along with their hope in this Christ, and [wish to perform] the eternal and natural acts of righteousness and piety, yet choose to live with the Christians and the faithful, as I said before, not inducing them either to be circumcised like themselves, or to keep the Sabbath, or to observe any other such ceremonies, then I hold that we ought to join ourselves to such, and associate with them in all things as kinsmen and brethren. But if, Trypho, I continued, some of your race, who say they believe in this Christ, compel those Gentiles who believe in this Christ to live in all respects according to the law given by Moses, or choose not to associate so intimately with them, I in like manner do not approve of them. But I believe that even those, who have been persuaded by them to observe the legal dispensation along with their confession of God in Christ, shall probably be saved. (Chapter 48)
Here we see a fascinating discussion in which Justin acknowledges that there are some who observe the law (confirmed much more strongly by Chrysostom later), along with faith. He extends fellowship to them, but doesn't want them to compel Gentiles. This is similar to what we saw in the book of Acts.
However, if some gentile Christians are compelled to keep various observances, he still thinks they will likely be saved (because they are acting in faith, not legalism), but doesn't like it too much.
So we see a growing apart of the two groups to a degree, and continued skepticism of gentiles being compelled to observe Jewish law.
Later this was present to an even greater degree and I would say some overreact.
John Chrysostom, Commentary on Galatians. 4th century
NPNF1-13. Saint Chrysostom: Homilies on Galatians, Ephesians, Philippians, Colossians, Thessalonians, Timothy, Titus, and Philemon - Christian Classics Ethereal Library
You will now understand why Paul calls circumcision a subversion of the Gospel. There are many among us now, who fast on the same day as the Jews, and keep the sabbaths in the same manner; and we endure it nobly or rather ignobly and basely.
Chrsysostom has stronger statements, but this will suffice.