Shake Off The Dust

And whosoever shall not receive you, nor hear your words, when ye depart out of that house or city, shake off the dust of your feet. Verily I say unto you, It shall be more tolerable for the land of
​Sodom and Gomorrha in the day of judgment, than for that city. Mat. 10:14-15

To shake off the dust from the feet, therefore, was a significant act, denoting that they regarded them as impure, profane, and paganish, and that they declined any further connection with them.

​Christ said that their punishment will be more “tolerable” - that is, more easily borne - than that of the people who reject his gospel. The reason is, that they were not favored with so much light and instruction. See Mat_11:23-24; Luk_12:47-48. Sodom and Gomorrah are often referred to as signal instances of divine vengeance, and as sure proofs that the wicked shall not go unpunished. See 2Pe_2:6; Jud_1:7.

In using this reference to Sodom and Gomorrah Jesus was using it as a description of what those cities represent:
The sin of the Sodomites was single, but that of those rejecting the apostles would be manifold, including
(1) infidelity;
(2) disobedience;
(3) ingratitude;
(4) inhospitality;
(5) rebellion and contumacy against God, contrary to the law of nature, and in defiance of the grace of God.

It is useless to ask the Lord to put forth His great power and save us, so long as we have made it practically impossible for Him to do as we ask. Even Jesus came to places where it was impossible to do any mighty works...and he marveled at their unbelief. Faith is only developed, when the conditions are met for it to grow; a willing spirit, a receptive mind, and a heart that desires to seek after the things of God. If none of this is present-even God cannot change the situation, or the people. He will not override people's free will.
Mar 6:4  But Jesus said unto them, A prophet is not without honour, but in his own country, and among his own kin, and in his own house. 
Mar 6:5  And he could there do no mighty work, save that he laid his hands upon a few sick folk, and healed them. 
​Mar 6:6  And he marveled because of their unbelief. And he went round about the villages, teaching.