Mark 6:11 (Jesus said to his disciples) But if any place refuses to welcome you or listen to you, shake its dust from your feet as you leave to show that you have abandoned those people to their fate.
I think Jesus was saying here that you can only do your best. People have to be ready in their hearts and that part is up to them. We have all heard that you can't help an addict until they want help. You can only do your part by spreading the word that "Jesus loves you!" The rest is up to the other person. There are so many people that need to hear about how much they are loved and we don't need to loose the opportunity to share that love because we keep on keeping on when somebody isn't open to the wonderful love that God has for all of us. Just before this verse in verse 4 Jesus said "A prophet is honored everywhere except in hos own hometown and among his relatives and his own family." Sometimes we just have to accept that it is not us they are going to hear. That is a good time to pray that God send somebody else in our place. Somebody that that person is open to. Because we walk away doesn't mean we give up. Often we forget how powerful prayer is. So when we get up and shake the dust off our feet we can walk away knowing we did our best then let prayer do the rest.