Even though I'm for marriage equality -- next week I'll be filing a brief supporting the challenge to the marriage laws of Oklahoma and Utah in the U.S. Court of Appeals for the Tenth Circuit -- I have no problem with Arizona's SB 1062.
SB 1062 does nothing more than align state law with the federal Religious Freedom Restoration Act (which passed the House unanimously, the Senate 97-3, and was signed by President Clinton in 1993). That is, no government action can "substantially burden" religious exercise unless the government uses "the least restrictive means" to further a "compelling interest." This doesn't mean that people can "do whatever they want" -- laws against murder would still trump religious human sacrifice -- but it would prevent the government from forcing people to violate their religion if that can at all be avoided. Moreover, there's no mention of sexual orientation (or any other class or category).
The prototypical scenario that SB 1062 is meant to prevent is the case of the New Mexico wedding photographer who was fined for declining to work a same-sex commitment ceremony. This photographer doesn't refuse to provide services to gay clients, but felt that she couldn't participate in the celebration of a gay wedding. There's also the Oregon bakery that closed rather than having to provide wedding cakes for same-sex ceremonies. Why should these people be forced to engage in activity that violates their religious beliefs?
For that matter, gay photographers and bakers shouldn't be forced to work religious celebrations, Jews shouldn't be forced to work Nazi rallies, and environmentalists shouldn't be forced to work job fairs in logging communities. This isn't the Jim Crow South; there are plenty of wedding photographers -- over 100 in Albuquerque -- and bakeries who would be willing to do business regardless of sexual orientation, and no state is enforcing segregation laws. I bet plenty of Arizona businesses would and do see more customers if they advertised that they welcomed the LGBT community.
At the end of the day, that's what this is about: tolerance and respect for other people's beliefs. While governments have the duty to treat everyone equally under the law, private individuals should be able to make their own decisions on whom to do business with and how -- on religious or any other grounds. Those who disagree can take their custom elsewhere and encourage others to do the same.