This is a strong verse, and it cuts both ways. I think of David, who supported King Saul, even when Saul sought to kill David.
Romans 13:1-2 New American Standard Bible (NASB)
Be Subject to Government
–Every person is to be in subjection to the governing authorities. For there is no authority except from God, and those which exist are established by God.
Therefore whoever resists authority has opposed the ordinance of God; and they who have opposed will receive condemnation upon themselves.–
But in some rare cases, civil disobedience was appropriate:
Acts 4:19–20 (ESV)
19 But Peter and John answered them, “Whether it is right in the sight of God to listen to you rather than to God, you must judge, 20 for we cannot but speak of what we have seen and heard.”
Here is a good article on this topic:
I have not researched their ministry, but the article seems sound.