Easy answer
For a long time Catholics and Muslims, to name the two groups you did, have told Unitarians they cannot legally marry gays. Was that not a violation of the rights of Unitarians? How many people screaming religious liberty today sided with the Unitarians on that? I'm just pointing out this wasn't a consideration until the ox's horns changed direction. If religious freedom is so important, why didn't the Unitarians have it before Judge Posner?
Let me ask this about RFRA, it goes to something Utah put in their bill. If a gay couple go to the courthouse to get married, is there anything in RFRA that applies to the people who conduct civil ceremonies? in other words, will RFRA embolden a public servant to say "nope, I cannot do that"? I ask because Utah specifically wrote in their bill that a servant can refuse but all courthouses must have available during all business hours someone capable of marrying said couple. My first choice would be to get people into the 21st century, but I'll take that compromise (others here may not).
10 years ago if religious conservatives had come forward with the concept of "we'll give in on the ban if we can have freedom to choose to participate", I'll bet it would have been taken. Rather they wait until the war is lost and then ask to dictate the terms of surrender.
I will differ from many on my side here, even after all the rhetoric. I will remind you I am not a lawyer, so don't parse the terms used as if a lawyer wrote it. If a substitute to a florist/baker can be found that places no undue burden on the customer, I'm fine with that. I know many of my allies will not agree. Just telling a couple to go away isn't going to cut it for me. If the baker can have an arrangement with a nearby baker who will work, I have no problems with baker 1 saying "I am sorry but I cannot be your baker, I will take you order exactly as if I were and submit it to baker 2 who will then work with you". In a town like Bloomington, Columbus, Kokomo, Terre Haute; I have no real problem with the concept. It isn't my first choice, but it comes closest to everyone getting what they want. I have no idea what to do if the wedding is in Brownstown and the Brownstown, Seymour, and Bedford bakeries all say no. Suddenly we have a burden.
As much as I have complained about this law, I realize you are somewhat correct in its impact. I do think it was written "poorly" or "broadly", take you pick, in the hopes that some judge somewhere will read the intent they want. Until judges actually decide what this thing says, we can argue all day long about its application to civil cases. But the fact that this is the first law passed after a NM case that said RFRA did not apply to civil cases (in that state but it made news nationwide for that) makes that paragraph not seem completely innocuous. Maybe no judge in Indiana would possibly read it that way. But then I don't see how anyone decided Dred Scott made sense either. At a minimum it is in there to cause confusion.
I miss Mitch Daniels. I don't know what may have been different with this law but I can't help but think it would have been handled better.