On the New Hampshire law, and everybody getting wiggy about "religious organization" exemption.
What most people are saying, and what I've also said, is exactly true. Churches are not required to perform marriages, or even recognize marriages that violate their own religious beliefs. Take for example the Catholic Church which has some of the most restrictive rules regarding marriage. However, having worked with many catholics, there are several loopholes and procedures to work around a lot of those rules (such as how to get an annulment even if there are children).
What most people miss is the little known dirty secret of churches. They aren't all that high and mighty. Many churches in the US (not all, but I'm willing to be it's somewhere north of 50% of the church organizations) allow people to rent their property for functions, who may not be members of the church. Also, and here's the dirty part of it, they have been willing to perform marriages, with their clergy/ministerial staff performing the ceremony, if the couple makes a sizable donation to the church regardless of if the couple or family are members. And that's the problem.
See, once you do that, it becomes a "business function" and then you have to follow state laws on anti-discrimination. That is, as a church with church property, you may deny the satanist group who want to rent out the church pavilion in the park like setting of your lawn for a bar-b-que, but if you've rented to other organizations not affiliated with the church, that group can sue you for discrimination and win. It's happened (not with satanists but with groups that certain churches didn't like).
Now do you see their dilemma? They already have a history of performing marriages for hire by ignoring their own rules for the quick buck. They've set precedent. If the state allows gay marriages, and a gay couple ask to be married in the church, by the church officials, if that church broke their rules before and the gay couple can prove it, the church is in big do-do.
And it's all because they intentionally misled people that marriage is a religious institution and they allowed themselves to go the way of the money lenders with their own temples. All because they wanted the money.