First, James rejects the Pharisees argument for circumcision, but does require Gentiles, who are living outside Israel, to observe four conditions the Mosaic Law requires of Gentiles living in Israel. He also states Gentiles will hear Moses in the synagogue on the Sabbath. In other words, he does not add the Sabbath: it is a given they will continue the practice.
Second, Christians are to be imitators of God. The command to observe the Sabbath is a particular way in which that is done: work six days and rest on the seventh.
Third, Christians are to be imitators of Christ who observed the Sabbath.
Fourth, the command to observe the Sabbath is given before the Mosaic Law. As such it is similar to the blessing promised to Abraham. It is not altered by the Law.
Fifth, the Sabbath is a sign and an eternal covenant.
Since the Gospels each record incidents where Jesus was accused of violating the prohibition of work on the Sabbath, it is easy to overlook the question of obeying the proscribed actions:
“Six days shall work be done, but on the seventh day is a Sabbath of solemn rest, a holy convocation. You shall do no work. It is a Sabbath to the LORD in all your dwelling places. (Leviticus 23:3 ESV)
Four of the seven Gospel disputes over the Sabbath also report Jesus went to the synagogue [cf. Matthew 12:1-14, Mark 2:23-3:6, Luke 6:1-11, 13:10-17]. Two show Jesus went to the Temple [John 5:1-14; 8:59-9:16]. Only Luke 14:1-6 records a dispute which makes no mention of the synagogue or Temple. However, that event was at a meal.
While it is true Jesus disputed with the Pharisees over their interpretation of what was prohibited, there is no evidence Jesus disputed over what was proscribed. To the contrary, the Gospels show Jesus did what was required: He attended a Sabbath meeting. Given this, it is reasonable to conclude Luke's Sabbath meal took place after the synagogue service.
Furthermore, the Gospels record additional events which occurred on the Sabbath during which there was no dispute over working [cf. Mark 1:21-27, 6:1-2, Luke 4:16-30, 4:31-36]. These all took place in the synagogue. This is further evidence Jesus did what was required on the Sabbath, as He must if He was without sin. Nor is there anything to indicate Jesus did away with the requirement for a holy convocation. There is no reason to believe the disciples who observed the requirement with Jesus while He was alive, would stop after His death and resurrection.
Acts repeatedly states the disciples were in the Temple and Paul is repeatedly in the synagogue on the Sabbath (Acts 13:14, 44; 16:13; 17:2; 18:4). Repeatedly it states Gentiles were present to hear what was said. This is prima facia evidence the requirement to assemble on the Sabbath was being followed. There is no evidence anywhere in the New Testament that Jesus, his disciples, Paul, or the first Christians failed to meet on the Sabbath.
The Scriptural Basis of the Sabbath
Since the requirement to limit work to six days is repeatedly stated in the Mosaic Law, it is easy to overlook the basis for observing the Sabbath came before the Mosaic Law.
The first specific Sabbath observances took place before the Israelites arrived at Mount Sinai. One month after leaving Egypt, the people complained about a lack of food. In response the LORD provided manna. The manna fell for six days, but not on the seventh. That day was a holy Sabbath to the LORD:
22 On the sixth day they gathered twice as much bread, two omers each. And when all the leaders of the congregation came and told Moses, 23 he said to them, “This is what the LORD has commanded: ‘Tomorrow is a day of solemn rest, a holy Sabbath to the LORD; bake what you will bake and boil what you will boil, and all that is left over lay aside to be kept till the morning.’” 24 So they laid it aside till the morning, as Moses commanded them, and it did not stink, and there were no worms in it. 25 Moses said, “Eat it today, for today is a Sabbath to the LORD; today you will not find it in the field. 26 Six days you shall gather it, but on the seventh day, which is a Sabbath, there will be none.”
Moreover, failing to observe the Sabbath was considered a refusal to keep the LORD's commandments and laws, not the Mosaic Law:
27 On the seventh day some of the people went out to gather, but they found none. 28 And the LORD said to Moses, “How long will you refuse to keep my commandments and my laws? 29 See! The LORD has given you the Sabbath; therefore on the sixth day he gives you bread for two days. Remain each of you in his place; let no one go out of his place on the seventh day.” 30 So the people rested on the seventh day. (Exodus 16)
The Mosaic Law to remember the Sabbath is referring to what the LORD had already put in place before giving the Law to Moses. The Mosaic Law adds to observing the Sabbath:
8 “Remember the Sabbath day, to keep it holy. 9 Six days you shall labor, and do all your work, 10 but the seventh day is a Sabbath to the LORD your God. On it you shall not do any work, you, or your son, or your daughter, your male servant, or your female servant, or your livestock, or the sojourner who is within your gates. 11 For in six days the LORD made heaven and earth, the sea, and all that is in them, and rested on the seventh day. Therefore the LORD blessed the Sabbath day and made it holy. (Exodus 20)
The Mosaic Law adds two things to the Sabbath. First, what was solely the responsibility of the individual now has the added responsibility for those with authority. For example, before the Mosaic Law if a slave attempted to collect manna or worked on the Sabbath, the slave violated the Sabbath. After the Mosaic Law, a slave owner also violated the Sabbath if their slave worked, even if the owner did not work. The second addition is a reason for the Sabbath: creation. God's people are to imitate the pattern God used to create.
Paul's letters to the Corinthians and the Ephesians give instruction to imitate Christ and God:
Be imitators of me, as I am of Christ. (1 Corinthians 11:1)
Therefore be imitators of God, as beloved children. (Ephesians 5:1)
God worked six days and rested on the seventh. Observing the Sabbath is a particular may to imitate God. Paul observed the Sabbath; Christ observed the Sabbath. The instructions are clear: the Church is to observe the Sabbath.
A Sign and a Covenant
The Mosaic Law added to the LORD's commandment and it explained the Sabbath is a sign of sanctification and an eternal covenant:
12 And the LORD said to Moses, 13 “You are to speak to the people of Israel and say, ‘Above all you shall keep my Sabbaths, for this is a sign between me and you throughout your generations, that you may know that I, the LORD, sanctify you. 14 You shall keep the Sabbath, because it is holy for you. Everyone who profanes it shall be put to death. Whoever does any work on it, that soul shall be cut off from among his people. 15 Six days shall work be done, but the seventh day is a Sabbath of solemn rest, holy to the LORD. Whoever does any work on the Sabbath day shall be put to death. 16 Therefore the people of Israel shall keep the Sabbath, observing the Sabbath throughout their generations, as a covenant forever. 17 It is a sign forever between me and the people of Israel that in six days the LORD made heaven and earth, and on the seventh day he rested and was refreshed.’” (Exodus 31)
The Antioch Dispute
The context of the Jerusalem Council begins in Antioch:
1 But some men came down from Judea and were teaching the brothers, “Unless you are circumcised according to the custom of Moses, you cannot be saved.” 2 And after Paul and Barnabas had no small dissension and debate with them, Paul and Barnabas and some of the others were appointed to go up to Jerusalem to the apostles and the elders about this question. (Acts 15)
Gentiles who became Christians, were told they needed to be circumcised. Paul, Barnabas, and others disputed this. As is clear in Galatians, Paul vigorously refuted the need for Gentiles to be circumcised. However, with respect to the Sabbath, this dispute says nothing about whether the Centile Christians were already observing the Sabbath. If they were imitating Christ and God, then it goes without saying they were to continue the practice of meeting on the Sabbath.
In fact James implies the Gentiles were already observing the Sabbath:
For from ancient generations Moses has had in every city those who proclaim him, for he is read every Sabbath in the synagogues.” (Acts 15:21)
Given the importance of the Sabbath, the Pharisees would not ignore those actions. Rather, this statement indicates James fully expected the Gentiles would continue the practice of meeting on the Sabbath. There was no added instruction to continue this practice, because none was needed.