Mark 6:11
And whosoever shall not receive you, nor hear you, when ye depart thence, shake off the dust under your feet for a testimony against them. Verily I say unto you, It shall be more tolerable for Sodom and Gomorrha in the day of judgment, than for that city.
The instruction takes effect when people refuse both to welcome the messengers themselves and to listen to their teaching and message. In that case the messengers are to depart and leave that place, shaking off the dust from under their feet as a testimony against the people and place that rejected them. The act sets a solemn limit on the reception of the gospel message, impressing its importance upon minds and warning that rejection brings accountability.
That rejection brings accountability in the day of judgment, when judgment will be more tolerable for Sodom and Gomorrah than for the city or place that rejected the messengers. The instruction applies not only to a single city or town but to expulsion from a whole region or district. Such expulsion comes when opponents stir up influential people through prejudice and false reports in order to drive the messengers out.
Labor is not to be spent without judgment, so discernment is to be used as to whether a household is worthy to receive instruction and support. Obeying the instruction in the face of persecution for the work or expulsion gives no cause for discouragement. Instead it calls for rejoicing, because being reviled and persecuted for Christ's sake brings great reward in heaven, even as the prophets before were so persecuted.