Indiana's anti-gay law isn't fooling anyone because we've seen this dance before
Crystal O'Connor, whose family owns Memories Pizza in Walkerton, Ind., told local TV station WBND that their Christian beliefs would prevent them from catering a same-sex couple's wedding.“If a gay couple came in and wanted us to provide them pizzas for a wedding, we would have to say no,” O'Connor told the news station.
Ever since the 60s, conservatives have tried to come up with some bullshit "principled argument" that just so happens gives businesses the power to oppress people and destroy them socially and economically in order to uphold rigid social and economic hierarchies. Barry Goldwater was really the master of this, creating this entire schtick arguing that while he was no racist, he had a "principled" belief that private business should be allowed to discriminate on the basis of race and that the CRA was illegitimate because it trod upon this sacrosanct right. The argument was a loser then and it's a loser now. Part of that is because the "principle" in question doesn't make sense. It asserts, without evidence, that people have a right to violate the social contract while benefiting from it, that they have a right to set up shop and take advantage of all the ways that society and government aid them---building roads so people can get to your business, providing electricity and water, that sort of thing---but that you should be able to renege on basic responsibilities of good citizenship.
People who make these kind of libertarian arguments try to convince you that they worked forward, starting with a premise (private business is sacrosanct) and working towards a conclusion (therefore business owners should be able to deny service to people on the basis of race or sexual orientation). Often they'll even pretend, Goldwater-style, that they are sad that they are forced, as deeply principled people, that it has to be this way, but that the continuation of racism/homophobia is simply an unfortunate and unavoidable consequence of their deeply held principles.
This bullshit fools roughly no one, as far as I can tell. It's cleanly obvious that what's really going on is that they are starting with a conclusion---that discrimination should be legal---and working backwards to rationalize it. You can tell this because the "libertarian" argument is always a last defense when a corrupt, bigoted social system is being successfully challenged. For instance, with segregation, pro-segregationists demanded segregation in all aspects of American life. It wasn't just lunch counters, but public buses and public schools. It was only when the momentum for desegregation built---and they realized that they were losing on the school and buses front---that they suddenly discovered this "principled" belief in the sacred nature of private business. It was nakedly obvious that the reasoning was, "Well, we can't segregate schools and buses, but is there some way we can at least keep them out of our restaurants?"
Same thing with the anti-gay argument. For decades now, conservatives have gleefully supported government discrimination against LGBT people. They argued that the government should deny them marriage licenses and that the government should police their private sexual behavior. Now that this is a losing argument, all of a sudden they pull this "principled" private business argument out of their asses, pretending that they aren't anti-gay, but just deeply concerned about religious business owners and their supposed rights.
This shit doesn't work. It didn't work then and it doesn't work now. The political support for discrimination is never about libertarian principles and it never swings on libertarian arguments. It's a very simple formula: If a majority of Americans support anti-gay bigotry/racism, then anti-gay and racist policies will continue to be popular. If the majority starts to find these views distasteful or embarrassing, they will support legal desegregation, and will not be very interested in conservative hair-splitting between public and private institutions.
If you're unconvinced on this front, I recommend reading Ed Kilgore's history on this issue, where he explains how conservatives pulled the same bullshit justifying racist policies in the 60s and 70s, including invoking the "religious liberty" to racially discriminate, that they are pulling on LGBT people now. Frankly, it suggests that this kind of disingenuous straw-grasping, if anything, backfires. Such naked lies might turn people off, because it reeks of desperation. Contrast this with the more successful attempts to convince the public that attacks on women's rights are not sexism but about "life" or "family". Those lies are just confusing enough that they tend to work better at muddying the issue and reducing opposition.