It has nothing to do with gay. It has everything to do with the legislature hijacking power from the judiciary by writing new laws.
In fact, the "anti-gay" bills are as much pro-gay as anti-gay. If an anti-gay person can discriminate against homosexuals, homosexuals can discriminate against the anti-gay fundamentalists.
The political optics are bad enough that reasonable people can rule out any social agenda. The obvious agenda pertains to conservative mistrust of the unelected, often-progressive judiciary.
Why do people keep saying this? That's not what the text of the Arizona bill allowed for at all. The discrimination allowed under that bill was very much a one-way street.