I can't understand how this is such a political issue are people really in here quoting the Federalist papers? (I consider it a dubious sign when people start quoting political papers as if they were somehow law, which happens far too often)
It is simple, if you operate a for profit business and you think that blacks originate from the descendants of Caine and are servants of Satan and you refuse to serve them you are breaking the law (and are also crazy). If you operate a Church or a Church business (like a Catholic School for example) then you can discriminate because you are a religious institution.... So why should blacks have protections and not LGBT people?
If religious freedom gives you the "freedom" to cripple our civic institutions (and yes, with the way our country is ran for profit companies are not only civic institutions, they form the backbone of civic participation) Then I am absolutely opposed to such "Freedom". If someone wants to discriminate against me because I am Trans, Lesbian, White, or even Atheist that person better be part of a church or some other exclusive affinity group, not a for profit enterprise.
As to the specific point, this bill was about taking democratic rights away from the cities of Arizona, several of whom have passed nondiscrimination laws. This entire thing was just another example of rural politicians trying to override the democratic processes of urban areas, because they can't seem to stand just discriminating against the LGBT community in their own back yard they need to do it in urban areas too.