Those "special rights" being.....?
The whole "protected class" concept found in the New Mexico law. Apparently as long as you are in a "protected class" you get the ability to screw people over who do not agree with you.
Again, when it comes to government or emergency services, there should be zero discrimination based on anything. Remember the constitution restricts what GOVERNMENT can do, not what PEOPLE can do (except own slaves or bring booze into a dry juristiction). Laws are designed to restrict what people do, limited by the constitution.
Laws like those in New Mexico appear to have a noble goal, but all they do is forment resentment, and retard the gradual shift in moral beliefs that would occur if these protected classes would go with persuasion and argument as opposed to governmental fiat.
Actions against government discrimination are one thing, and through this debate I can see the reasoning for allowing gay marriage, or at least the changing of marriage by the state into a union contract, with the concept of marriage left to religons and/or other private secular organizations.
But I have to draw the line at laws, commissions and fiats that force individual people in non essential tasks to have to take on business relationships that go against thier moral compass. The couple in queston suffered no financial loss and did not enter into a contract with the photographer that was broken at a later date. The only thing they had was thier feelings hurt. To judge against people whos only fault was to be honest about thier beliefs, whos service to society at a whole is non essential is to me a horrible form of tyranny.