[alakazam]

Well, they argue that the government is taking away their rights to religious choice because they are forcing them to do services for gay marriage, a thing that goes against their religion. Christian bakeries were fined for refusing to bake cakes for gay marriages. If a Christian's beliefs tells him that he will go to hell if he mingles with sinners, and the government forces him to mingle with gay people, then there is a problem because that means that he is deprived of his freedom of choice.