If the wedding photography is a “business establishment that provides or offers its services...or goods to the public”, then it is, by legal definition, a “public accommodation”.
Does this make sense to me? No, but it is the law. There seem to be more details, based on size of business, etc - but it is entirely possible that under NM law, a wedding photography business cannot deny service to two homosexuals having a ‘wedding’.
The Human Rights Commission has already ruled so. I suspect the Courts in NM will rule likewise...but like I said, I’m not a lawyer.
I shouldn’t have used the words ‘public business’ - that unnecessarily confused the issue. However, many people do not understand that their ‘private business’ is probably a ‘public accommodation’ - that certainly isn’t the meaning of the word that comes to my mind.
Then every civil litigation attorney or law firm is in violation of the law, because they routinely refuse to take cases because the either believe that the plaintiff's claims are spurious, the defendant has no legitimate defense, or either classification of litigant does not have the resources to pay for the services.
Checkmate.
As I noted before, you cannot make a blanket declaration that you have a right to refuse service under your freedom of religion because you know that somebody has committed sins.
EVERY ADULT ALIVE ON THE PLANET has committed sins. Therefore, such a blanket declaration is merely a pretext and not a legitimate religious objection.
You do, however, have a right to refuse service under your First Amendment freedom of religion right if that service involves your active participation in such a sin, as defined by your religion.
Let's say that you are a photographer and that you hire out to photograph social gatherings.
A black group wants you to photograph a checkers playing tournament. You turn them down because they are black.
That is discrimination. It is based on factors EXTERNAL to you and factors that are even addressed by Federal Civil Rights laws.
A black group wants you to photograph a checkers playing tournament. You turn them down because, to make some religious point or other, they are playing checkers with consecrated hosts they have pocketed after attending Catholic Mass. You are Catholic. What they are doing is a sin according to the Catholic religion and you absolutely refuse to be an active participant in that sin.
That is absolutely protected by your First Amendment rights to freedom of religion. It is based on a factor that is exclusively related to how YOU practice YOUR own religion. The race, creed, color, sexual orientation or ethnicity of the other party is irrelevant to the issue.
In regards to state laws, whatever the laws of New Mexico or California or Massachusetts are in regards to the issue is totally irrelevant as the Supremacy Clause of the Constitution makes them so:
The "Constitution and the laws of the United States...shall be the supreme law of the land...anything in the constitutions or laws of any State to the contrary notwithstanding."