And when they opposed themselves, and blasphemed, he shook his raiment, and said unto them, Your blood be upon your own heads; I am clean: from henceforth I will go unto the Gentiles. Acts 18:6
Shaking the raiment and throwing dust and ashes on the head is a general custom among Easterners. When men wish to renounce or repudiate certain people or ideas or deeds, they shake off the outer robe from the front. This signifies that they are through. This custom is similar to the shaking of dust from the sandals. Some men take a little dust or a stone and throw it away, stating, “I have no part in it.” Where there are no sandals nor stones to be found, people shake off their outer garments as proof of repudiation. Moreover, when people relinquish certain responsibilities or disagree on important matters, they generally shake their garments, to signify that they will have nothing further to do with the matter in question.
Paul hitherto had obeyed the command of his Lord and the apostles. From the outset he preached first to the Jews. But when he saw that the Jews were stubborn, he changed his plans and warned them that he would begin to preach to the Gentiles, that is, Arameans, Greeks and Romans.
Hitherto, Paul had been sincerely seeking the Jews and the descendants of the Ten Tribes, preaching to them in the synagogue and in the homes of the converts. Even as a prisoner in Rome he first preached to the Jews in their synagogue. Paul was zealous to help his people to understand and accept the truth of Jesus’ gospel. Like Jesus, he sought his own, but they rejected him.
(Lamsa, George. New Testament Commentary, A.J. Holman Co., Philadelphia: 1945, pgs 131-132)