DUSTY FEET

As the apostles went forth to spread the Gospel, they encountered both hospitality and hostility. The Lord gave instruction concerning the latter ... If a place will not welcome you or listen to you, as you go out from there, shake the dust off your feet as a testimony against them. (Mark 6:11)

In other words, Jesus gave His disciples permission to declare God's judgment upon that house or village. Shaking the dust off their feet infers that ... 'you had an opportunity to hear the message of salvation but you spurned it; we leave you to the consequences'. When someone's mind was firmly set against the Lord, they were to turn their evangelistic efforts elsewhere.

It is important to understand that Jesus was not speaking about those who are slow to believe. He is infinitely patient with sinners ... The Lord is not slack concerning His promise, as some count slackness, but is longsuffering toward us, not willing that any should perish but that all should come to repentance. (2 Peter 3:9)

MacArthur - It is not that we are to turn away from those who reject the gospel at first hearing or even after several hearings. Had that practice been followed, many believers would not be in the kingdom today. Were God not marvelously patient and long-suffering with fallen mankind, He would have destroyed the world long ago. 

But ... 

Those who defiantly reject the truth are not to hinder one's mission of spreading the Gospel. Shaking the dust off one’s feet is similar to the phrase 'I wash my hands of it'. It is a symbolic indication that one has done all he can and therefore carries no further responsibility. Jesus told His disciples they were free to walk away with a clear conscience. 

Paul and Barnabas put Christ's words into practice. They had been preaching in Antioch when some of the Jewish leaders stirred up persecution and had them expelled from the region ... So they shook the dust off their feet as a warning to them and went to Iconium. (Acts 13:51) 

There will be occasions when the Lord calls us to stand firm, proclaim truth, and give our testimony. Sometimes we are to patiently continue until we see results ... sometimes God gives us the freedom to move on. We figuratively 'shake the dust off our feet' when, under the Holy Spirit’s direction, we surrender people to the Lord and emotionally let go. 

You are only responsible for your obedience to God, not for the results of that obedience.