Acts 15 does not say that gentile Christians are expected to keep the seventh day. You may surmise that they went to synagogue to hear Moses preached by Jewish teachers if you want to yet the passage does not say that.
Then it seemed good to the apostles and the elders, with the whole church, to choose men from among them and send them to Antioch with Paul and Barnabas. They sent Judas called Barsab'bas, and Silas, leading men among the brethren, with the following letter: "The brethren, both the apostles and the elders, to the brethren who are of the Gentiles in Antioch and Syria and Cili'cia, greeting. Since we have heard that some persons from us have troubled you with words, unsettling your minds, although we gave them no instructions, it has seemed good to us, having come to one accord, to choose men and send them to you with our beloved Barnabas and Paul, men who have risked their lives for the sake of our Lord Jesus Christ. We have therefore sent Judas and Silas, who themselves will tell you the same things by word of mouth. For it has seemed good to the Holy Spirit and to us to lay upon you no greater burden than these necessary things: that you abstain from what has been sacrificed to idols and from blood and from what is strangled and from unchastity. If you keep yourselves from these, you will do well. Farewell." Acts 15:22-29 RSV
And the decision of the council (mentioned a few verses earlier in Acts 15) was worded this way:
Therefore my judgment is that we should not trouble those of the Gentiles who turn to God, but should write to them to abstain from the pollutions of idols and from unchastity and from what is strangled and from blood. For from early generations Moses has had in every city those who preach him, for he is read every sabbath in the synagogues." Acts 15:19-21 RSV
It is the Jews, not Christians, who preach Moses every sabbath (seventh day) in the synagogues. The passage makes no claim that Christians gathered in the synagogues with the Jews to hear the Jewish preachers preaching Moses. The truth is that the Jewish leaders in Jerusalem went out of their way to expell Christians from Jewish synagogues. Saul himself (later known as Paul) went to Damascus with the intention of arresting Christians to take them back to Jerusalem to be punished.
But Saul, still breathing threats and murder against the disciples of the Lord, went to the high priest 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. Acts 9:1-2 RSV
In the years after Saul's conversion Jewish synagogues were not welcoming places of worship for Christians. The Jews in Thessalonica actively opposed Paul's preaching. They even went to the trouble to travel to Beroea to make sure that he was not welcome there.
But when the Jews of Thessaloni'ca learned that the word of God was proclaimed by Paul at Beroe'a also, they came there too, stirring up and inciting the crowds. Acts 17:13 RSV
Nowhere in these passages is there any explicit statement that Christians went to synagogue with the Jews in these towns.