When we profess our belief in the Catholic Church, we are professing that she is the Church Our Lord built on the rock of Peter and that she teaches on account of God’s authority, not the authority of human beings (See Matthew 16:19, Matthew 18:18 and Luke 10:16 for example). So when the Pope intends to teach the Church or the bishop intends to teach his diocese, we recognize that authority by giving assent. This authority goes beyond borders and social status, and guides us on how we must live to have eternal life.
On the other hand, when we look at politics, we are looking at a finite system of government that promotes the common good of the people living in a nation. The laws are good when they support moral goodness, and bad when they do not. A government can give people what they want even though it is evil, and as a result govern badly even if it is popular. Ideally, a good government should have laws that promotes virtue and opposes vice—though we do not believe law should suppress every vice (see HERE). Politics and civil government deal with temporary things. Their policies only last as long as the government does, and it is easy for nations to become corrupted over time with the shared values they profess.
When you stack the two side by side, it is clear that wise Catholics ought to put the teachings of the Church above the laws of government when the two are in conflict. That doesn’t mean disloyalty to our country. We’re called to be good citizens and promote the common good. But we’re not to put the political platforms of a government (a finite good) above the state of our souls. So when Catholic citizens vote, or when Catholic members of government create or enforce laws, they need to approach these things with our eternal end in mind. When they don’t—when they insist on supporting politicians or laws which go against God’s commands—they fail in their calling as Christians and they fail in their tasks as citizens or government officials.
We need to make a distinction here. I'm not talking about circumstances which leads a Catholic vote to limit evil in order to prevent some of harm a corrupted government causes until a time when we can reverse the evil done. I’m talking about Catholic voters and politicians who support what the Church condemns as evil, even if they claim to personally oppose it. They are not only doing harm to their souls and those of others, but they damage society as well. That’s why we must oppose things like legalizing abortion or redefining marriage so it becomes a sexual relationship instead of building the family as the basic unit of society cause this damage.
Catholic voters need to identify the politicians who support the evils that do the greatest harm to souls and to society itself and oppose them. It’s not a matter of preference like ice cream flavors. Some of these politicians may also support things we do like. It’s a matter of looking at things like a Catholic, seeing the good and the evil and using prudential judgment on how to promote the good and limit the evil.
There can be legitimate differences of opinion. When there are only good candidates, people can have different thoughts on the better one. When there are only bad candidates, people can disagree on who is the greater evil. But we have to use the moral teaching of the Church, not our political agendas, to make that judgment. That means we look to the Church under the leadership of the Pope and bishops in communion with him to guide us. We don’t pick and choose from these teachings to excuse what we were going to do anyway.
When we make decisions on how to vote, we need to ask ourselves if we are voting this way to follow Our Lord through the teaching of His Church, or whether we are voting this way to support a political agenda which is incompatible with our calling as Christians. How certain are we that Our Lord will not condemn us at the Final Judgment?
If we don’t like the answer, perhaps we should pray and study and see if we can find an answer before going ahead.