Romans 13, the controversial chapter about obedience to government, should be read in context. The preceding chapter gives instructions for believers to "avenge not yourselves: but rather give place unto wrath; for it is written vengeance is mine; I will repay, saith the Lord" (Ro 12:19). The believer is then instructed to obey the rulers for they are ordained by God to be the avenger against evil-doers (Ro 13:1-4).
It is evident God set up government to keep the peace, to punish evil-doers and to protect the God-fearing people. The individual is not intended to take matters into his own hands: when he has been a victim of crime or of a civil offense, he is to take the matter to the governing authorities. In much the same way, the believer is to take grievances against fellow believers to the body of believers, the church, for mediation (Mt 18:15-17; 1 Co 6: 1-8).
In no way does the fact that God ordains government (or ordains church leaders, for that matter) alleviate those leaders from their responsibility to serve God and to lead in a righteous manner. Likewise, the people being governed have a responsibility to hold their leaders to a godly standard of conduct.
When leaders in the church turn out to be false shepherds, the congregation is warned not to follow them (2 Ti 3; 2 Pe 2; Jude). Neither should God's people follow wicked civil leaders. The idea that civil government is free from God's mandates is a perversion. Civil leaders are ordained by God to act righteously. If they do not, the righteous should act to remove them from leadership. The righteous; i.e., the believer, should not rely on a misinterpretation of Romans 13 to excuse himself from taking a stand against unrighteous leaders!