God gives us what we deserve. A nation makes laws that reflect the morality of the people. Politics is not our savior, Jesus is. All laws “legislate morality.” There is a difference between crime and sin.
Those are the short answers.
The longer answers are that a Christian legislator cannot enact God’s Law in the land without the positive participation of the majority of the people. He cannot pass a law, for instance, that says everyone has to go to his church on Sundays. This is not because it wouldn’t be a good law, but because no one would obey it. This is why prohibition was repealed.
What the legislator would have to do in order to pass a law about where folks should go to church is to have the vast majority of folks become Christians and want to go to his church. In the period where many people go to his church but not most, until the vast majority are interested in attending his church there will be great turmoil and strife in the land.
We see this happening with homosexuality right now. The sodomite coalition is gaining influence and power and is working hard to “convert” the American people to their views. Until they do, there will be strife and battles of every kind. And, because the sodomites are vile, nasty people they will use any weapon at their disposal to bully, cajole, and wrangle what they want, until they get it.
The problem is that they don’t really know what they want. But the Bible says they want chaos and every form of evil. But this destroys a nation and never builds it up. But I digress.
With regard to sodomite marriage (and beyond) the current law says that it is illegal for two homosexual men or women to marry. The real question is should the Christians vote to overturn that law? The answer is no! But we need to remember that because we are in a war, simply voting against it every year will not solve the problem. As long as the sodomites continue to preach and the Christians continue to flirt with and commit spiritual adultery with the world (even if it is in every area other than homosexuality), they will eventually join with the pagans and vote to overturn the laws. This is because unless Christians repent and turn to God themselves, down to the bone, they are as bad as the pagans and really worse because they know better. Their condemnation is justified.
So the answer to your question is “yes.” Christians should vote against laws that make evil more palatable and successful, but they need to know that politics cannot and will not save. Jesus saves and only as Christians preach the Gospel, by word and deed, praying that God would grant repentance to those experiencing the good news will society really be transformed.
I hope this helps,