I don't think anyone said the bill "mandated" anything. And of course everyone was free to not discriminate, and the vast majority would not, but that's not the point. The purpose of the bill (at least according to many proponents) was to give legal cover to discrimination by private entities against LGBT so long as they chanted some magic words about "religious beliefs." And it certainly expanded the circumstances when that discrimination could legally occur. These people pushing the bill weren't members of minority religions worried about using peyote or something - they were evangelicals, who bitterly opposed SSM and followed that loss up with this bill. Everyone knew the point of it.
And if the issue is liberty, then I see no reason at all to draw a line between discrimination for "religious" purposes and for any other purpose, against LGBT, blacks, Jews, women, fat people, Christians, whatever. Let's make it clear what we're allowing here and do away with the ridiculous requirement that the person can discriminate but only if his or her religion tells them it's OK.
Bottom line is if it's about liberty then anyone should be able to deny services to anyone for any reason or no reason at all. The libertarians are at least consistent on that point.