If you want to kill legislation that protects the right of Christians to withhold business services from same-sex couples, here’s one way to do it: Don’t warn people about Christians. Warn them about Muslims.

That strategy was on display in the campaign against Arizona Senate Bill 1062, which would have shielded businesses from discrimination suits if they acted on religious beliefs. Everyone understood that the bill would have allowed conservative Christians to refuse services for a gay wedding. But in Arizona, that wasn’t a strong enough argument against it. So opponents went for the Muslim angle.

Many Americans who talk about religious freedom are really just interested in the rights of conservative Christians. They’re not so keen on Muslims. In fact, they worry about Muslims imposing their beliefs on Christians. Two days ago, in praise of the Arizona bill, Rush Limbaugh complained, “Religious beliefs can’t be used to stop anything the left wants to impose—unless they’re Muslim religious beliefs, and then we have to honor those. But any other religious beliefs are not permitted.”

The first reference to Muslims in the Arizona fight, as far as I can tell, came from the Anti-Defamation League in a letter to state senators and in testimony before a state Senate committee on Jan. 16. If the bill were to pass, the ADL’s assistant regional director told the committee, “A Muslim-owned cab company might refuse to drive passengers to a Hindu temple.”

This week, as lawmakers voted on the bill and Republican Gov. Jan Brewer weighed whether to sign it, the chorus grew. On Feb. 20, the editorial board of the Arizona Republic warned Brewer, “The proposed law is so poorly crafted it could allow a Muslim taxi driver to refuse service to a woman traveling alone.” On Feb. 21, John Aravosis, the editor of Americablog and a political consultant, brought up the Muslim cab driver and other scenarios raised by the ADL. On Feb. 22, Box Turtle Bulletin, a gay rights blog, published a post titled “Did the Arizona Legislature Just Legalize Sharia Law?” The post noted that the bill

exempts anyone from having to follow a whole host of state laws, ordinances and regulations if they conflict with an individual’s religious belief. This would mean that a Muslim landlord could forcibly evict single women or a convert to Christianity, since either action would be covered by Sharia law. It would also allow a Muslim employer to treat his non-Muslim employees with the same rules as his Muslim employees. He could compel non-Muslims to work longer hours at lesser pay and reduced rank.

On Feb. 23, KTAR, a Phoenix news station, devoted a whole story to criticisms of the bill by a Scottsdale attorney. It began:

If Gov. Jan Brewer signs Senate Bill 1062, the service refusal bill, into law, one Valley attorney is afraid Arizona could face several legal challenges. “For example, a taxi cab driver who may be Muslim may refuse to give service to a woman who may be traveling without a male companion, in violation of their religious law” …

On Feb. 24, USA Today columnist Owen Ullman asked, “if religious beliefs are a justification for refusing gay couples, shouldn’t Arizona extend the principle to all religious beliefs? Devout Muslims should have the right to refuse service to women who are not covered in burqas.” On Feb. 25, fellow columnist Kirsten Powers, a former communications consultant, added:

Say the only pharmacy in town is owned by a conservative Muslim. He believes that women should be covered. A mother comes in to get antibiotics for her sick child. He refuses service unless she covers herself. Will the religious right defend this? …

What if an Army sergeant in full regalia is driving through a small town and his car breaks down and it’s too late to find a mechanic? There are two hotels in the town; both are owned by pacifist Christians. Do the backers of this bill really believe it should be legal for him to be refused a room and forced to sleep in his car?”

I can’t prove that all this Muslim talk influenced Brewer’s decision to veto the bill last night. But it definitely caused trouble. During the state Senate debate on Feb. 20, the bill’s sponsor struggled with the Muslim taxi driver question. (Skip to minute 1:22 of the video.) On Feb. 25 the state’s Capitol Media Services raised the taxi driver scenario in an analysis of the bill’s legal ramifications. On Feb. 26, CBS News asked the president of the Center for Arizona Policy, which helped craft the bill, whether it would “protect a Muslim wedding photographer who does not want to photograph a Jewish wedding.” She said it would.

I don’t think it’s an accident that some of the folks who played the Muslim card were political professionals, or that they threw in the Army sergeant scenario for good measure. When you’re trying to get lawmakers and a governor in a conservative state to kill a religious freedom bill, pleading for gay people or fretting about Christian overreach may not cut it. It might even backfire. If you can find some other scenario to talk about—preferably one in which Christians or soldiers pay the price for a minority’s religious freedom—you’re more likely to give the majority pause. It’s an ugly game. But that’s how you play it.