Acts 13:42 So when the Jews went out of the synagogue, the Gentiles begged that these words might be preached to them the next Sabbath.
The first place Paul and Barnabas preached was in the synagogue for the Jews because that is what was probably expected of them.
The people obviously came out of the synagogue talking about everything which had been said and the Gentiles wanted to hear all about this truth because they were normally left out of things!
Jesus did not say the disciples had to go to all the Jews only and tell them the truth. He did not say discriminate so we have a pure race. Jesus said go out into all the world and preach the gospel.
That is why Paul and Barnabas went out to all people!