"But when [Paul and his party] departed from Perga, they came to Antioch in Pisidia, and went into the synagogue on the Sabbath day and sat down. " (Acts 13:14)
"Now it happened in Iconium that [Paul and Barnabas] went together to the synagogue of the Jews, and so spoke that a great multitude both of the Jews and of the Greeks believed. " (Acts 14:1)
"Then Paul, as his custom was, went in to them, and for three Sabbaths reasoned with them from the Scriptures, ... Then the brethren immediately sent Paul and Silas away by night to Berea. When they arrived, they went into the synagogue of the Jews." (Acts 17:2,10)
"And [Paul] reasoned in the synagogue every Sabbath, and persuaded both Jews and Greeks." (Acts 18:4)
"And [Paul] came to Ephesus, and left them there; but he himself entered the synagogue and reasoned with the Jews." (Acts 18:17)
"And [Paul] went into the synagogue and spoke boldly for three months, reasoning and persuading concerning the things of the kingdom of God." (Acts 19:8)
Take it up with Paul. In every place he would first go to the Jews in their synagogue, and then, when he was rejected, he would go to the gentiles. No doubt this provoked the Jews to even more animus against Paul.
The reason He went to the synagogues was not to preach to the Jews....but the Gentiles. The Jews just happened to also be there because the Gentiles worshiped on the Sabbath also......with them.
Don't you see this simple scripture lesson regarding the Sabbath worship of the Gentiles?
Why did he not just say to the Gentiles as he entered the synagogue...."Hey boys, let me finish up with these Jews...and I'll catch you all tomorrow?" the reason is obvious. The Gentiles also worshiped on the Sabbath!
"So Paul still remained a good while. Then he took leave of the brethren and sailed for Syria, and Priscilla and Aquila were with him. He had his hair cut off at Cenchrea, for he had taken a vow. And he came to Ephesus, and left them there; but he himself entered the synagogue and reasoned with the Jews." (Acts 18:18,19)
Notice how it say that when Paul came to Ephesus, he left Priscilla and Aquila behind, and went to the synagogue alone. Now this is an odd statement if the synagogue was the church, and a legitimate place of Christian worship.
Why would Paul leave his fellow Christians behind while he went into the synagogue if it was a true place of worship?