People seem to be conflating two different things:
1. Refusing to serve gays because they are gay. A gay person goes into a bakery, asks for one of those croissants in the display case, and the owner refuses to serve that person solely because they are gay. This is what most people seem to be imagining.
2. Refusing to participate in/support an event that goes against one's religious beliefs. Similar bakery, but now someone (straight or gay) asks for a wedding cake for a gay wedding (with two grooms on top, say). If the baker has a religious belief that opposes gay marriage, must they still provide the cake?
Expanding on #2 a bit:
- What if the bakery customer is a Satanist, and wants a cake with a graphic depiction of a virgin sacrifice, or a ritual orgy, or something like that?
- What if it's a church rather than a bakery; should a gay couple be allowed to force a pastor to perform a gay wedding, even if that goes against the church's teachings? Most people would say no, but where's the line between a church and a bakery? What if the bakery is run by a convent? This is similar to the situation in front of the Supreme Court, with the Obamacare contraception coverage waiver.
As others have mentioned, the Arizona bill doesn't directly mention sexuality at all, so it's not immediately obvious whether it only addresses case 2 or if it also covers case 1. But they're clearly different, and it would be nice if more people would recognize that.