After telling the Twelve to stay in whatever house welcomes them until they leave that town, Jesus now tells them what to do if they can find no one to welcome them.
The Jews on returning home from Gentile territory would before they entered the borders of their Holy Land would shake the Gentile dust from their feet so as not to contaminate their sacred space.
“Whatever town or village you enter, search there for some worthy person and stay at their house until you leave. As you enter the home, give it your greeting. If the home is deserving, let your peace rest on it; if it is not, let your peace return to you. If anyone will not welcome you or listen to your words, leave that home or town and shake the dust off your feet. Truly I tell you, it will be more bearable for Sodom and Gomorrah on the day of judgment than for that town.” (Matthew 10 v 11-15)
Today you may want to move on and yet you believe God wants you to stay and that is right that you be obedient. Jesus is not saying that today wherever you are you must not persevere.
But Jesus has said they must travel light and now must keep going and if they get hurt by not receiving a warm welcome then to do what is culturally the practice at that time and remove the dust. Don’t contaminate your future by the rejection you are now receiving.
However, if you are not being made welcome and you are unable to stay then move on so long as you can move on without taking hurt with you.
So before they go they know that they will experience failure with some people and towns that they take the gospel to. Some places fail and it isn’t anything to do with the minister.
The problem is many move on carrying hurts and bitter memories with them. They never shook the dust off and as a result make a mess for the people they meet ahead of their path.
Some go through life having the same arguments but with different people simply because of the dust on their feet.