Pizzagirl. Your questions sound like a law school exam. 
Also, just so you know, I find the law offensive, but that is not legally binding. It does remind me of a situation 20+ years ago when I was shopping for my wedding dress. The boutique owner said that she had to close her store one day so that a man could come in and try on a wedding dress. She wasn’t thrilled, but I think she relented because she could not resist a sale. Anyway…
I’m certainly not an expert in this area of law. But, here’s how I’d start.
Caveat: I haven’t read the IN statute and have no interest in doing so. But one would start there and look at the legislative history to see what “intent” Indiana lawmakers claim as basis for the exercise of their legislative power. Legislative power originates from the state constitution, so that’s the starting place to see where there might be some basis for a challenge to the law.
My immediate and very general thoughts:
(1) A private businessperson has the right to do anything with his property unless the commercial activity is in contravention of some law. We have free enterprise unless there is a prohibition (big can of worms which we’ll leave closed for now). “I own a shop. I cannot be forced to do what is against my beliefs.” We know the law prohibits me from refusing service to people on the basis of race (violation of Federal equal protection laws). But I can refuse service to people if they come in shirtless or shoeless (permitted by local health and safety laws).
(2) If my business practice is offensive to some interest, and there is enough public support, a law gets passed. Let’s call that another “prohibition.” So, I refuse to bake a cake for you that celebrates something I do not agree with religiously. I claim I am expressing my religious beliefs. Does that fly? Indiana says yes.
(3) Is that a state law (a) in violation of the U.S. Constitution, i.e., it violates some fundamental right of others that is also or already protected (free speech, privacy rights, equal protection, etc.) or (b) that runs afoul of Federal preemptive prohibitions (like regulations of accommodations because Congress can regulate interstate commerce)?
I hope the ACLU starts looking into the law.
But, for now, try economic sanctions.