There is no such thing as a lawful wedding when there is no divorce prior to what would be a 2nd marriage of one or both parties. There is no State in the nation that legally permits bigamy.
New Mexico is a rare State that has no laws that either specifically prohibit or permit gay marriage.
If this photographer was asked to photograph a gay wedding , they can refuse to do so based on their religious convictions by making the true statement that there is no room in their schedule to photograph the ceremony. And there is nothing that can be done about that.
A wedding photographer, licensed as what some call a public accommodation and that exclusively photographs weddings can refuse to photograph what is not a lawful wedding by definition. Because their license denotes they accommodate lawful wedding ceremonies only.
Show me the law that you're referring to where it says a wedding photographer is compelled to photograph an illegal bigamist wedding.
There is no law that can force a photographer, or anyone else that could be retained, to accommodate an unlawful ceremony. Not one.
And a couple, be they straight or gay, who would seek to take legal recourse against someone who did refuse is just asking for not only a counter suit but a State charge when they seek to bring a charge against that public accommodation that refused their request. Because bigamy is illegal.
If one partner in the proposed ceremony is still married while seeking to enter into a lawful marriage, they're breaking the law. They'll be prosecuted. Not the public accommodation that refused their request to participate in a bigamous ceremony.
And since there is no law that permits gay weddings in New Mexico, an exclusive service for wedding photography only can refuse to photograph a gay wedding when there is no law that says gay weddings are lawful in New Mexico.