That verse taken in it's proper context tells us to not have a judgmental attitude towards others. One who wlaks in the Spirit (in submission to and in the power of the Holy Spirit judges all with a right heart and understanding (Rom 13:1).
As far as legal authorites they are ordained by God Himself:
Rom 13:1 Let every soul be subject unto the higher powers. For there is no power but of God: the powers that be are ordained of God.
Rom 13:2 Whosoever therefore resisteth the power, resisteth the ordinance of God: and they that resist shall receive to themselves damnation.
Rom 13:3 For rulers are not a terror to good works, but to the evil. Wilt thou then not be afraid of the power? do that which is good, and thou shalt have praise of the same:
Rom 13:4 For he is the minister of God to thee for good. But if thou do that which is evil, be afraid; for he beareth not the sword in vain: for he is the minister of God, a revenger to execute wrath upon him that doeth evil.
Rom 13:5 Wherefore ye must needs be subject, not only for wrath, but also for conscience sake.