"They're restricting the our freedom to ..."
If the Catholic Church can complain that a law restricts their right not to purchase health insurance if it covers birth control because it conflicts with their belief, doesn't a law that forbids gay marriage restrict some churches' freedom to allow gay marriage?
Just wonderin'
= new reply since forum marked as read
...it just restricts those marriages from being legal. It's like the legality of divorce. That it's legal doesn't stop the churches from saying it's wrong and not recognizing that divorce and refusing to marry a divorced person. So it's legality (or non-legality) in the state doesn't impinge on their religious practices. Similarly, the legality of this law (personally, I don't see it as legal, but that's for the courts), doesn't impinge on some other religion marrying gays even if the state doesn't recognize the marriage.
Now if the law had it that police had to arrest any religious minister performing a spiritual gay marriage and/or those participating in it, THEN it would impinge on their religious freedoms. Just as the fact that certain drugs are illegal arguably impinges on the religious freedom of religions that use such drugs in their religious ceremonies.
Of course, I get the hypocrisy of the church crying foul over the insurance yet not crying foul over this, but we know that the churches are blind to their own hypocrisy--of if not, happy enough to maintain it. You'd have to be stone stupid not to recognize that the leaders of such churches don't really want religious freedom, they want a christian theocracy and only play the religious freedom card when they think they can portray themselves as a persecuted minority. 
...seem like he's curtailing their rights and freedoms or is going to to. He could say he likes bunnies and they'd argue that he's planning on making it illegal for hunters to kill rabbits. Remember when he asked for Dijon mustard and they jumped on that as his being elitist and foreign? They'll grab at any straw, pull at any comment like a gambler at a slot machine in hopes that it gets them a jackpot.
But what's that go to do with your question about whether the NC law restricts religious freedom?