The expression shake the dust off your feet
echoes the ancient Jewish practice to, upon returning to their homeland from visiting a Gentile area, carefully remove all the Gentile, unclean
dust from their shoes and clothing. For the apostles, this was a symbolic action, expressing that they saw even the Jewish residents of the town as Gentiles: as not being part of the true Israel (see Acts 13:51)
The expression used by Jesus in Matthew 10:14 reminds us of the ancient Jewish practice to, upon returning to their homeland from visiting a Gentile territory, carefully remove all the dust from their shoes and clothing because of the fact that they considered the Gentile land as unclean. For the apostles, this then served as a symbolic action intended to express that they regard even the Jewish residents of the town as Gentiles: that is, as not being part of the true Israel (see Acts 13:51).1
11 Dans quelque ville ou village que vous entriez, informez-vous s'il s'y trouve quelque homme digne de vous recevoir; et demeurez chez lui jusqu'à ce que vous partiez.