A primary belief in Christianity is the obedience to the Lord. The logic is the obedience to the higher authority, imply civil persons obey the government, and the government obey the Lord. That is to say, if the government did not obey the Lord, they will be punished by the Lord, whereas the civil persons will be punished by the government if they were against its authority.

Romans 13:1-7 is often debated with Acts 4:19;
> 19 But Peter and John replied, “Which is right in God’s eyes: to listen to you, or to him? You be the judges!

How to reconcile these apparently conflict ideas?

A mistake is generally taken when one think himself a representative of God, and take action against the government in the righteous way of his imagination, that violate the Lord's sovereignty. Based on Peter's word, if the government forced Christians to do something against his belief, Christians must not do it, but that doesn't imply Christians must overthrow the government in order to stop the suppression, or put themselves as if having a privilege not to fulfill a civil duty that everyone had to comply. 

It is likely in Paul's opinion, if someone did not obey the government, they likely did not obey the Lord as well. Why would Jesus accept unjust persecution? For obedience to the Lord, and endurance in life save humanity.