"Lawmakers justifying the resurrected bill cited a handful of incidents across the country in which business owners were sued for refusing to provide services to gay couples. One notable case was that of a New Mexico photographer who refused to take pictures of a gay commitment ceremony because, she said, it violated her religious convictions."
It's called freedom of speech. Business owners are free to exercise it as long as they do not discriminate against employees. It was portrayed as an anti- LBGT law by people who like to shove federal authority in everyone's asses to force THEIR agenda.