By going out of our way to do good to people who are also following Jesus, we set in community an example of love in behaviour that is winsome. The law Christ gave us was to love one another, which is something we do tangibly with actions, and intangibly by disposition. Perhaps this is why it is especially for the household of faith.

Since the most loving thing a Christian can want for people who don’t know Jesus is to effect a saving introduction, then this is a vicarious act of service. It would be difficult to convince someone of the reality of the good news about Christ if we were to refuse to serve the very people who teach us about it, and with whom we claim brotherhood. The dissonance would equate to disgrace, so we must treat those of the household of faith with special care, and not cause others to stumble. This is essentially “walking by the Spirit”, or as James puts it:

if anyone is a hearer of the word and not a doer, he is like a man who looks intently at his natural face in a mirror. For he looks at himself and goes away and at once forgets what he was like. But the one who looks into the perfect law, the law of liberty, and perseveres, being no hearer who forgets but a doer who acts, he will be blessed in his doing. If anyone thinks he is religious and does not bridle his tongue but deceives his heart, this person’s religion is worthless. Religion that is pure and undefiled before God, the Father, is this: to visit orphans and widows in their affliction, and to keep oneself unstained from the world…

Entire chapter here:
http://www.gnpcb.org/esv/search/?q=gal+6&src=esv.org