The book Acts tells about the disciples spreading the Gospel often in the face of opposition from various groups including government bodies. In chapter 4 of that book, Peter and John are brought before the Council and forbidden from spreading word of Jesus.
Acts 4:13 Now when they saw the boldness of Peter and John, and
perceived that they were uneducated, common men, they were astonished.
And they recognized that they had been with Jesus. 14 But seeing the
man who was healed standing beside them, they had nothing to say in
opposition. 15 But when they had commanded them to leave the council,
they conferred with one another, 16 saying, “What shall we do with
these men? For that a notable sign has been performed through them is
evident to all the inhabitants of Jerusalem, and we cannot deny it. 17
But in order that it may spread no further among the people, let us
warn them to speak no more to anyone in this name.”
I don't know that this quite answers the question, because I'm not sure how official this prohibition was, but it seems to get to the heart of things. I believe the response of Peter and John provides a good template for Christians:
Acts 4:19 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.”
I'm also reminded of Shadrach, Meshach, and Abednego, who while in Babylon refused to bow down to Nebuchadnezzar's statue (Daniel 3), and similarly, Daniel, who defied Darius's decree and continued to pray to God daily (Daniel 6).
I think the key to all these passages is that our allegiance is primarily to the authority of God, but that the governments is still authoritative secondarily next to that. When the two seem to conflict with one another, the examples set seem to show that God's followers are not called to be revolutionaries, but rather to obey the laws of the land as much as their conscience will allow.