"We should have a federal law that says under no circumstance, in any jurisdiction in the United States, will Shariah be used in any court to apply to any judgment," Gingrich said in a September speech.
A group called Act! For America ran a radio ad in Oklahoma supporting the initiative. "Help us stop Shariah law from coming to Oklahoma," the narrator said, "to protect all Oklahomans -- non-Muslims and Muslims alike -- from the tyranny of Shariah law."
But Rev. Barry Lynn of Americans United for Separation of Church and State says that such sentiments could have unintended, negative consequences, opening the debate about whether courts should reconsider deference to any religious ideals in areas such as family or probate law.
"This opens a huge set of doors raising questions of whether in wills, in medical decision making, or in property distributions, any religious motives can be considered," Lynn said.
"We may see that if judges cannot acknowledge the presence of an Islamic principle in a decision that they can't note Christian, Jewish or other religious either."
In his lawsuit's court papers, Awad of the Council on American-Islamic Relations wrote: "The initiative's architects have variously referred to State Question 755 as a preemptive strike, a response to a looming threat, and as a much needed legal reinforcement to the Oklahoma's Judeo-Christian values."
Leslie Griffin, who teaches constitutional law at the University of Houston Law Center, said outlawing Shariah law could lead to sidelining Christian and Jewish "laws" as well.
The use of Orthodox Jewish decision-making bodies known as "Beth Dins" to settle family law disputes is an example, Griffin said.
"Once you question using Shariah law in any circumstances, you must also question using any other religious law as the basis of a legal decision," she said. "When courts allow married couples to resolve their disputes in a religious tribunal, like the Beth Dins, the same principle seems to be at stake."
She said the Oklahoma initiative could have nationwide implications.
"What we've seen from history is that there is never just one little case about a new religion," she said. "A new religion brings lots of questions to the courts. The issues will be working themselves out across the country."
Of the ballot measure, Lynn of Americans United for Separation of Church and State said, "This is a real expression of overt hostility toward one religion tradition and the personal decisions made by its believers or its practitioners."
There are only a handful of cases in which a judge has referenced Islamic law in a decision.
One 2008 New Jersey case has garnered the most attention from Gingrich and Act! For America. A woman known as S.D. sought a temporary restraining order from her husband, who she claimed had raped her.
A trial judge found that the husband lacked criminal intent for the sexual contact because he was "operating under his [Muslim] belief that it is, as the husband, his desire to have sex when and whether he wanted to was consistent with his practices and it was something that was not prohibited."
An appellate court reversed the ruling, finding the defendant's behavior illegal "regardless of his view that his religion permitted him to act as he did."
"We respect the Constitution, and the law of the land," Awad said. "However, we shouldn't be precluded from engaging in religious practices that don't break the law."