It makes it easier to accept the imperfections of others. Jesus made it a point to accept the service of imperfect people, because there aren't any other kind. He chooses to live in them. Look for Him in them. Actively seek the criticism of others who are clearly wiser than yourself, those who know Jesus better.
Civility is a part of righteousness.
It's not that Jesus would demand high etiquette, but that we place some value on social stability. Sometimes, this requires withholding the truth. An obvious example is that you don't insult some lady with an outrageous hat visiting your church. Civility requires that you not blurt out your opinion of her headgear. You should never lie outright.