God has written his law, a sense of right and wrong, on human hearts. This is the basis for civil law, e.g., laws against murder, stealing, bearing false witness. See Romans 2:14-15: "For when Gentiles, who do not have the law [i.e., the Ten Commandments, given to Israel], by nature do what the law requires, they are a law to themselves, even though they do not have the law. They show that the work of the law is written on their hearts, while their conscience also bears witness, and their conflicting thoughts accuse or even excuse them. . . ."
As much as possible, civil laws and societal norms should correspond to God's Law, his unchanging will for human society. When they do, a society works better. When they don't, a society declines. In our lifetime, American society has declined especially in the areas of marriage and the family, sexual behavior, and the like. We can and should work for improvement in these areas, both in unwritten societal norms and in written civil laws.
Matters such as abortion and homosexual "marriage" (sic) fall under the category of Law. One need not be a Chrisitan to recognize that these things are wrong. Nature, reason, and conscience all attest that abortion and homosexual behavior are wrong. To oppose these abominations is not a distinctively Christian position.
What IS distinctively Christian is the content of the Gospel, e.g., the doctrine of the Trinity, the doctrine of the person and work of Christ, the doctrine of justification, the preaching of forgiveness and eternal life for the sake of Christ. This is the exclusive domain of the Church. This is the ministry of the Gospel.
The Law cannot save. Only the Gospel can do that. The Law can make for a better society, and it should do that.
One more post in a moment on what Michael Horton said.
Summing up my position (and what I think is close to Horton's): Homosexual "marriage," no. Contractual arrangements between individuals, already permissible. But no special status bestowed by society on immoral relationships.