My more right-leaning friends, Bill Keezer and Malcolm Pollack, have written their own posts on the Indiana religious-freedom law. Both posts are worth your time, even though Bill and Malcolm make clear that they stand on the opposite side of the aisle from me (well, Bill's opinion on the matter is more nuanced and not easy to summarize in a single sentence, so I'd advise you just to go and read what he has to say).
There are quite a few issues on which I lean right: economics, foreign policy, and education are among them. Because I have a gay relative, though, I tend to lean more distinctly leftward on this topic. I don't think the gay lobby, taken as a whole, is being overly shrill or oversensitive; I think the lobby's concerns are legitimate and should, at the very least, be discussed in a civil manner. But that's one major point of contention between left and right regarding this issue: how to frame the problem. What's the point of departure? Is this a religious-freedom issue? A gay-rights issue? A bigotry issue?
Bill's post is interesting because he sees this as basically a property-rights issue—which is, incidentally, how my own church, the PCUSA, framed the problem some years ago when discussing whether PCUSA churches should allow gay weddings on their grounds. Malcolm's post, meanwhile, notes that it would have been easier for the gay couples wanting wedding cakes and photos to find another provider instead of making a stink about the refusal of service (implicit in Malcolm's post is, I think, the idea that the market simply needs to work its work). But Malcolm's claim harks back to the question I asked in my own post, when I wondered aloud as to whether businesses run by religious people enjoy the same legal and moral status as religious institutions, like churches, that claim the right to refuse services on religious grounds.
My own feeling is that the very concept of a bakery is inherently secular, which means all bakeries should offer goods and services to the whole public, regardless of the staffers' personal religious convictions. A church might have the right to refuse a gay couple a wedding ceremony on its grounds, but a bakery run by socially conservative Christians isn't a church, and thus doesn't have the same right. I'm not sure how to articulate my position better; I'd need to delve more into the legal dimension before I can say more.
You might respond, "What about a bakery that exclusively makes cross-shaped cakes specifically for Christian churches? Should they be forced to cater to the general public when it's obvious that the general public isn't that bakery's market?" I honestly don't know the answer to that. My gut tells me that a bakery with the skills to make specially shaped cakes can easily alter its style to accommodate anyone making any request, and there's also the thorny issue of forcing a provider to provide something that's "not on the menu," so to speak.
There's also this objection: "Should a Christian-themed bakery be forced to make a wedding cake for a satanist wedding?" This question more obviously highlights the religious-freedom issue. (Side note: Satanism and other such "evil" religions* also present problems for those of us who are religious pluralists, but that's a topic for a different post.)
It's a tangle, to be sure, and I object to anyone who thinks the issues surrounding the Indiana law and other RFRAs are easily soluble. They aren't. Which is why there's a debate at all.
*Many satanists object to the "evil" descriptor, saying that their religion is primarily about hedonism, not the active promotion of evil, heinous acts. Take that for what it's worth.