While some Christians may disagree, it is commonly recognized by many Christians that to demand a Christian provide goods and services or otherwise participate in a gay marriage ceremony would be sinful. The reason comes from scripture. The apostle Paul wrote that pressuring a Christian to do something he believes is sinful is to commit a sin.
"The one who observes the day, observes it in honor of the Lord. The one who eats, eats in honor of the Lord, since he gives thanks to God, while the one who abstains, abstains in honor of the Lord and gives thanks to God," Paul writes at Romans 14:6-7. He concludes at verse 23 with, "But whoever has doubts is condemned if he eats, because the eating is not from faith. For whatever does not proceed from faith is sin."
If a Christian in good conscience believes that to engage in an act would be sinful, trying to pressure the Christian into that act would be sinful in itself. This applies to nebulous matters not clearly addressed in scripture. Paul makes clear there are things that are absolutely, indisputably sinful. "But now I am writing to you not to associate with anyone who bears the name of brother if he is guilty of sexual immorality or greed, or is an idolater, reviler, drunkard, or swindler -- not even to eat with such a one. For what have I to do with judging outsiders? Is it not those inside the church whom you are to judge? God judges those outside. 'Purge the evil person from among you.'" (1 Cor. 5:11-13)
While many non-Christians quote "judge not lest ye be judged," scripture makes it absolutely clear Christians are to judge those within the church who are engaging in clear sin. If someone holds himself out as a Christian, but is unrepentant in sinning, other Christians are to shun him lest he reflect on the church as a whole.
Everything above is commonly accepted Christian orthodoxy. In matters of no clear Biblical authority, if someone believes an act is sinful, he should not be pressured into that sin. But those who believe it is sinful are not to judge those who think the act is not sinful. In matters that are absolutely, objectively in the Bible considered sinful, Christians are to judge their fellow Christian and disassociate from him unless he repents and turns from his sins.
A lot of Christians who believe everything written above as it applies to gay marriage have come to the conclusion it does not apply to American politics. Right now there are Christians in America who believe they should not vote for a man who calls himself a Christian, brags about his affairs, and swindles the elderly and single moms out of money. These same Christians also believe they should not vote for a woman who supports the right to kill children.
But other Christians are hellbent on pressuring these conscientious objectors into voting. Politics are not a subject from which one can remove one's faith. There is no obligation in Christianity to vote. In fact, it is a rather good thing to not collaborate in the political process if doing so might prop up those who hold themselves out as a Christians while openly celebrating sin. The right to not vote is as powerful as the right to vote and the most important thing is to not violate your conscience. We may all be sinners, but Christians do not endorse sins, they repent.
If a person wants to vote in the presidential election, let them. But if someone refuses because their conscience tells them none of the candidates are worthy of support, pressuring them to vote is as much as sin as violating one's own conscience. Our country is not eternal, but we are and will be called one day to account.