I should add that responding to a same-sex ceremony that way (booked for the day) after being told it is a homosexual union is just baiting the gay/lesbian zealots. They easily can call later to book a traditional marriage and get scheduled. Then you are trapped in a lie and their next stop is the lib-created Human Rights Commission.
Freedom of religion is a principle that supports the freedom of an individual or community, in public or private, to manifest religion or belief in teaching, practice, worship, and observance; the concept is generally recognized also to include the freedom to change religion or not to follow any religion.
Forcing people of faith to betray that faith is government not only redefining that person's religious belief but forcing them to become party to an event that's defined as sinful by that person. In the case of the photographer, the NM Human Rights Committee has essentially told the Christian photogs that they must engage in a pagan festival, a direct violation of their beliefs. In the case of an inn keeper there's less leeway because they're not engaging in a gay couple's sinful actions. This type of discrimination is the same as racial discrimination. Finally, there are provisions for conscientious objectors in time of war, so the concept of not forcing people of faith into sinful action is not without precedent and practice in the US.