This episode of Paul and Barnabas's ministy includes the "shaking the dust of their feet" piece. This is a phrase that often means something like, "give up on someone," perhaps someone who has been unreceptive to the gospel. It was also a ritual that Jewish people used to show that they were separated from Gentiles, so the using of the action to show digust with Jewish leaders might have been specifically for them. Those who sought to weaponize religion wielded their influence in that city, and Paul and Barnabas recognized the limits of their abilities, and the need to find more receptive ears.