Of course that depends on what is defined as "matters of faith and morals", doesn't it? The LDS defined polygamy as a matter of faith - did the State allow them to continue or did the Mormons have to redefine that matter of their faith? A church may have as a matter of morality something that the State calls illegal, the same for matters of faith. It boils down to who is the authority, God or man? We believe it is God, first, and then the powers that God ordained to govern. We can know whether or not a matter of faith and morals comes from God because we have His sacred Scriptures that spell it out for us.
When the first Christians were condemned to martyrdom for refusing to bow to the gods of Rome or to forsake Jesus as the Son of God, it WAS the State imposing its ideas of faith and morals onto the believers in Christ (for that really IS what a "church" is made up of) and they chose to obey God rather than men. Subordination in some things of the faithful to the State IS honoring to God since He says that the powers that be derive that power from Him and do not bear the sword in vain. When the State usurps the authority of God by their ungodly pronouncements, God WILL deal with them. In the meantime, in order to live peaceably with all men, we should strive to live honest and moral lives so that the cause of Christ is not blasphemed and there can be no legitimate accusations of wrongdoing made against us.
Let's not lose track of the origin of this current argument. Popes do NOT have a monarchical authority over nations. The clerics do not rule over the State. Popes do not have a God-given right to ordain or depose kings. Therefore, they are every bit as liable as any other person to obey the laws and ordinances of man and certainly to those of God.
The same Church that in Romans 13 was calling the State the minister of God's purposes, was calling it a demonic entity by Revelation 13. All of the Apostles but one was martyred; yet the Apostles and their successors never counseled sedition: they did not take up arms even to defend their families and congregations.