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!
Do you actually read any of these accounts before spouting off? It says he went in to reason with the Jews.
"Now when they had passed through Amphipolis and Apollonia, they came to Thessalonica, where there was a synagogue of the Jews. Then Paul, as his custom was, went in to [the Jews], and for three Sabbaths reasoned with them from the Scriptures, " (Acts 17:1,2)
The fact that there were gentiles there is a secondary considertion. When the Jews would not hear him in the synagogue, he went directly to the gentiles.
"And [Paul] reasoned in the synagogue every Sabbath, and persuaded both Jews and Greeks. ... But when [the Jews] opposed him and blasphemed, he shook his garments and said to them, 'Your blood be upon your own heads; I am clean. From now on I will go to the Gentiles.'" (Acts 18:5,6)