In instructing The Twelve to shake the dust off their feet in places where they are not welcomed or listened to, Jesus may be warning them of the contagious nature of unbelief and how at moments of weakness we can be susceptible to its influence when witnessing unbelief in others. However, this can also be understood as encouraging discretion in striving to understand the mysteries of our faith. For although faith and reason are not in opposition, this does not mean that our intellects have the capacity to encompass God or fully understand the mysteries of our faith. Thus, when tempted to doubt some Christian truth or mystery because we simply cannot understand it, we need to discern when to continue wrestling with these deep questions as a means to a deeper and richer faith, and when to desist and, shaking the dust of unbelief from our feet, step back into the safe refuge of faith and trust in the God who will continue to reveal himself to us in love.
Dennis DiVito says
In addition, I think that “shaking the dust off your feet” also refers to knowing when others are not ready to be open to the Way. Like when Jesus left his home town when he revealed himself, it is better for us to leave people alone when they are closed minded or closed hearted. It is not for us to to change them, it is for God.