Is this being rude, especially for men of good will spreading a message of peace? No, because in the ancient East, "salutes" meant making an extensive stop full of questions between participants asking how life is, how the family is, how the kids are, how many are in your clan, etc. until you know as much about the other person as you do about your neighbor. In light of the urgent message of the Kingdom, the admonition is roughly equal to telling travelers not to make extended, distracting stops while on an urgent mission.