This chapter records the beginning of a planned strategy of taking the message of Jesus to other places. Saul, who is now referred to as Paul, is part of that plan. What is seen here is a pattern through Paul’s travels. Being Jewish, Paul starts by telling Jews about Jesus and then transitions to non-Jews (Gentiles).
There is nothing wrong with taking Jesus to those we are comfortable talking to, but it is important not to stop there. I’m sure Paul would have preferred talking to Jews, with whom he shared common traditions and values. But he also talked to non-Jews who practiced religions and lifestyles he found offensive.