The religious freedom law says the government cannot intrude on a person's religious liberty unless it can prove a compelling interest in imposing that burden and do so in the least restrictive way. This law simply was not necessary. The US Constitution already does that admirably. The state law can trump local non-discrimination laws, and sooner or later - likely sooner - some florist shop or for profit wedding chapel will refuse service to gays and lesbians for religious reasons.
There will almost certainly be a state legal case to determine if the action is covered under the new law. Then there will be an appeal, regardless of the ruling - either from the religious or those they discriminated against - to the SCOTUS if necessary, which is where the state law will almost certainly be ruled unconstitutional. Legal eagles amongst us, please weigh in with your insight.
As I stated, this is a political move by a right wing fundie GOP politician trying to set himself up for a national office run in the near future. This stuff disgusts me. Lawyers in love.