In Matthew chapter 10 we see that Jesus sent His disciples out to reach out to the Jews.
He said, “Don’t go to the Gentiles or the Samaritans, but only to the people of Israel—God’s lost sheep. Go and announce to them that the Kingdom of Heaven is near” (verses 5-7).
Then in Matthew 10:14 Jesus says, “If any household or town refuses to welcome you or listen to your message, shake its dust from your feet as you leave”.
Why did Jesus tell his disciples to shake the dust off their feet if a city or home didn’t welcome them?
Apparently it was a custom for pious Jews when leaving Gentile cities. They shook the dust from their feet to show their separation from Gentile practices.
If the disciples shook the dust of a Jewish town from their feet, it would show their separation from Jews who rejected their long awaited Messiah.