1 Maccabees 2:34 "But they said, 'We will not come out, nor will we do what the king commands and so profane the sabbath day.'" 

We have a duty to obey lawful authority under the fourth commandment, that's what keeps worldly order from the descending into chaos. So, generally, if the king commands something, even if it's something we don't like, we are to do it as long as it is moral. But our primary duty is to God, so when the king's commands conflict with God's, then we must disobey the king, even if that means our life is on the line. This is the story of martyrs up and down the centuries, like St. Thomas More, for example, whose life is a very good reminder of our obligation to God over our king. 

Understanding when we are to put God over king is a function of being properly ordered, understanding the proper hierarchy of obedience. Earthly power is corrupting, so it is not uncommon for the commands of earthly leaders and kings to contradict God's commands. The devil will try to play on our understanding that we are to obey proper authority and convince us to go along with our leaders' commands, even when they contradict God's. We can be convinced that our understanding of God's commands is incorrect, or flawed, or we are being too strict and "religious", especially when many other of our fellow citizens, even fellow Catholics, are going along to get along. Often these people will work against us, too. In our times, this includes most of the media, and the great power of social media. Those who follow the "kings" of our world, the authority figures of our time, may try to ridicule, ostracize, and punish those who do not go along, but we must not let them get to us.

When we are obeying God over king, we are in the right, and we will, ultimately, be vindicated, even if it is not until after our death. The martyrs, again, are our role models here. When in doubt, look to them!