Several times in the New Testament Jesus tells his disciples to shake the dust off of their feet when a town rejects them and their message of salvation (i.e. Matt. 10.14, Mark 6.11, Luke 9.5, and Acts 13.51). In his commentary on Luke 9.5, Joel Green has a nice summary of what this means.
“…Jesus warns them [the disciples] of the possibility of rejection, which he himself had experienced (e.g. 4:28-30), by advising them on how to respond in the case of the refusal of hospitality. ‘Dusting of the feet’ was an act connected to ridding oneself of defilement, such as when one had traversed Gentile lands. Ordinarily an action related to self-purification, here it is specifically interpreted as a performative testimony against the village – designed not, then, to render the traveler clean (again), but to declare the village ‘unclean.’ That is, Jesus’ instructions, albeit in a subtle way, circumvent ordinary rules of purity by turning them on their head. Jesus performed no such act of self-purification upon his return from the land of Gentiles and the domain of the unclean in 8:40, for he had found responsive faith even in the midst of impurity and rejection (8:26-39). No longer working narrowly with an ethnic definition of Israel as the people of God, he now declares that those who refuse the salvific visitation of God – present not only in his [Jesus'] ministry but also in the extension of his ministry via these twelve envoys – are to be regarded as though they were outside the people of God. As in jesus ministry so with the apostles,’ to receive the kingdom of God was to receive its heralds.”
With that in mind, read Paul’s sermon in Pisidian Antioch in Acts 13. There many of the Jews reject, revile, and persecute Paul and Barnabas even though the Gentiles received the message of salvation with joy and gladness. Paul and Barnabas left Pisidian Antioch after shaking the dust off their feet. They weren’t shaking the dust off their feet because they came into contact with “unclean” Gentiles. They were shaking the dust off their feet as a symbol that the unbelieving Jews had “thrust aside” the word of God and judged themselves to be unworthy of eternal life (Acts 13.46). Or, in the words of Luke Timothy Johnson, “Those who reject the kingdom are themselves rejected from it.”
The above quote by Green was taken from page 360 of his NICNT commentary on Luke.