This column originally appeared in the Daily Beast. It has been republished with the author's permission.

Ben Carson's blunt remarks about a Muslim president triggered much outrage, even after he partially walked them back. But secular Muslims like me, who reject political Islam, understood what he meant: He doesn't want a Muslim as president who doesn't believe in the strict secular separation of mosque and state, so that the laws of the state aren't at all touched by sharia, or Islamic law derived from the Quran and hadith, the sayings and traditions of prophet Muhammad. Neither do we. We really don't want a first lady—or a president—in a burka, or face veil.

Carson's comments underscore a political reality in which Muslim communities, not only in far-flung theocracies like Saudi Arabia and Iran, but also in the United States, still struggle with existential questions about whether Islam is compatible with democracy and secularism. This struggle results in the very real phenomenon of "creeping sharia," as critics in the West call it (and which some Muslims like to mock as an "Islamophobic" allegation). While the U.S. Constitution's First Amendment states the United States "shall make no law respecting an establishment of religion," the Quran states that Allah "takes account of every single thing (72:28)," which has led to the divine mandate by leading Muslim scholars to reject secularism, or alamaniya, or the way of the "world," derived, from the Arabic root for world, alam.

In too many instances, we are seeing an erosion of those boundaries, in part led by some Muslims, increasingly using America's spirit of religious accommodation and cultural pluralism to challenge rules that most of the rest of America accepts. Many of those incursions have been led by the Council on American-Islamic Relations (CAIR), a controversial self-described advocacy group for Muslims that, not surprisingly, called for Carson to step down this week.

For example, when I was a girl in New Jersey in the early 1970s, we took our Muslim holidays off, if we wanted, but didn't demand the rest of the school take the day off with us. Last week, however, four decades later, New Jersey Muslims stormed out of a Jersey City school board meeting after the school board refused to cancel school at the last minute for the Muslim holiday called "Eid al-Adha," or "the Feast of Sacrifice," being celebrated Thursday. CAIR has lobbied public school officials for the change for the sake of "diversity and inclusion."

At the meeting, the local NBC news segment showed an older woman yelling in Arabic that the holiday was her "right," followed by a young Muslim woman, wearing a headscarf and smiling eerily as she said, "We're no longer the minority. That's clear from tonight. We're going to be the majority soon."

The thinly veiled threat was as disturbing to me as it might be to other Americans. Unspoken is the sharia ruling that Muslims engage in no work or school on the day of Eid-ul Adha, but, instead, as the prophet Muhammad is quoted as saying in a hadith, "O people of Islam, these are days of eating and drinking."

Yet it is unreasonable and, quite frankly, selfish for Muslim parents to demand an unplanned holiday, forcing other parents to scramble to find child care, as board member pointed out. But, sadly, on the eve of the "Festival of Sacrifice," there is one issue that too many Muslims find difficult to sacrifice: Their belief that mosque and state must not be separated but must in fact be intermingled.

Tthis month, an ExpressJet flight attendant, Charee Stanley, a relatively new convert to Islam, demanded the Equal Employment Opportunity Commission reinstate her job after she was put on leave for refusing to serve alcohol. CAIR argued the flight attendant deserved "a religious accommodation."

But Ali Genc, senior vice president of media relations at Turkish Airlines, said in an interview that his carrier, based in a Muslim country, doesn't make such allowances, saying, "The service and consumption of alcoholic beverages onboard is regulated in the framework of the rules of Turkish Airlines. In this respect, a refusal of such service by our cabin crew is not possible as a matter of course."

Some years ago, a Muslim woman, Ginnah Muhammad, demanded her right to enter a Michigan small claims courtroom with a face veil, a demand that was correctly refused. CAIR supported her petition, saying removing the veil meant denying the woman her "constitutional rights."

Before that, another Muslim woman convert, Sultaana Freeman, sued the Florida Department of Highway Safety and Motor Vehicles to allow her to take her driver's license photo with her veil. CAIR supported her demand, saying the woman "sincerely" believed it would "advance her piety." These efforts at appealing to schools, courts, and other government structures to suit hyper-conservative interpretations of sharia reveal how some Muslims are going too far in demanding accommodations by U.S. authorities, blurring the mosque and state divide.

Corey P. Saylor, director of the "department to monitor and combat Islamophobia" at CAIR, disputed my argument that the organization has worked to erode secularism in the United States, saying, "CAIR's legal and political advocacy aims to preserve our nation's spirit of religious accommodation from efforts to erode it or restrict it to certain faiths."

It's not "time to pull the plug" on Carson's campaign for his indelicate comments on Islam, as columnist P.J. O'Rourke argues. But it is time to continue the politically incorrect but critical conversation that he started.

He added, "Americans of the Islamic faith have equal rights and responsibilities in civic life and may argue for policies they favor, and win or fail based on a well-established political and legal process to which everyone has, and should have, equal access."

In the cases that I cited "the courts or relevant political entities make the final decision," Saylor said, "not us." Indeed, fortunately, CAIR has so far lost its Florida, New Jersey and Michigan efforts.

Carson wasn't being hyperbolic in expressing concern. Globally, Muslims express deep problems with separation of mosque and state. In a 2013 Pew Research Center survey, an alarming percentage of Muslims worldwide, numbering 99 percent in Afghanistan and 45 percent in Russia, answered "favor" when asked whether they favor or oppose making sharia the law of the land. A disturbing percentage supported including sharia in family, marriage, and criminal law, including settling property disputes, deciding child custody arrangements, stoning people for adultery, and cutting off the hands of thieves. While to be sure the survey wasn't conducted in the West, the results reveal cultural mindsets.

In the United States, I first confronted our Muslim community's difficulty with the concept of secularism in late 2003 when I walked through the front door of my mosque in Morgantown, West Virginia, citing Islamic rights as well as civil rights granted me as a woman in this country. Soon after, the Pittsburgh Post Gazette wrote an article that included this passage: "Dalía Mogahed, outreach coordinator for the Pittsburgh mosque, agrees on Muhammad's respect for women but says Nomani is viewing the issues through the eyes of a secular feminist rather than the eyes of a Muslim."

Secular feminist?

I read the passage twice because to me, being a secular Muslim feminist wasn't a contradiction in terms. To me, though they are few and far between, we have Islamic theologians who advocate for equal rights for women and secularism in governance. But the criticism was a wakeup call to me of the challenges we face advocating for secular values among Muslims. (Mogahed later led survey research at Pew and was a member of an Obama administration advisory council. She didn't return a request for comment.)

It's not "time to pull the plug" on Carson's campaign for his indelicate comments on Islam, as columnist P.J. O'Rourke argues. But it is time to continue the politically incorrect but critical conversation that he started.

The presidential candidate is talking against a backdrop of 9/11 and a reality in which political Islam expresses itself violently in the West and in Muslim countries from Iraq to Indonesia. To me, not acknowledging this real issue among Muslims amounts to another Carson allegation, of Muslims practicing taqiyya, or deception.

Much of the modern-day debate dates back to 1977 when Yusuf Al-Qaradawi, a theological brain trust of the Egyptian Muslim Brotherhood political party, fighting secularism, wrote, "Al-Hulul al Mustawradah wa Kayfa Janat 'alaa Ummatina," or "How the Imported Solutions Disastrously Affected Our Ummah," casting secularism and Islam in a cosmic battle, with a section entitled, "Secularism vs. Islam."

He wrote: "Secularism may be accepted in a Christian society but it can never enjoy a general acceptance in an Islamic society." Today, even ordinary Muslims ask questions like, "Is it permissible to pray behind imams who...promote democracy and secularism?" The answer from too many in Muslim leadership is no.

Carson dared to address an explosive issue that Muslims are still struggling to resolve on issues of sharia and fiqh, a related concept, referring to Islamic jurisprudence. Not long ago, Ayad Jamal Deen, a former Iraqi parliament member and courageous intellectual and religious cleric, admitted, "In my opinion, the fiqh is more dangerous than nuclear technology." He acknowledged that "Islam has been politicized and is used as a sword." We would be wise to listen to advocates of secularism who have battled the forces of political Islam.

In his Fox walk-back interview, Carson said, "Now, if someone has a Muslim background, and they're willing to reject those tenets and to accept the way of life that we have, and clearly will swear to place our Constitution above their religion, then of course they will be considered infidels and heretics, but at least I would then be quite willing to support them."

To me, Carson's words aren't "anti-Muslim" either, as a Guardian headline described them. They are a realistic mirror on the challenges Muslims today face with the notion of strict secularism.

Even John Esposito, founding director of Georgetown University's Prince Alwaleed bin Talal Center for Muslim-Christian Understanding, funded by a rich member of the theocratic Saudi ruling family and criticized for publishing "apologist" explanations of Islam, wrote not long ago:

"Many Muslims, in particular Islamists, cast secularism as a completely foreign doctrine imposed on the Islamic world by colonial powers." Even "secular reformers" who appreciate Western secular democracies "opt for a state that reflects the importance and force of Islamic principles and values as they proceed to engage in wide ranging reformist thinking."

Interestingly, for secularists, like Iraqi-born Faisal Saeed Al Mutar, founder of the Global Secular Humanist Movement, raised by a liberal Muslim family and now living in New York City, it's actually strict secular Muslims who could truly understand the critical need for a separation of mosque and state. He said in an interview that he doesn't agree with Carson's edict and noted, "I would also argue that secular Muslims would make the best presidents on the topic of the First Amendment because they understand the most [that] the marriage between religion and politics is very poisonous."

One of his Facebook friends responded: "Faisal Saeed Al Mutar for President." Meanwhile, some of his Muslim critics have also called him a "heretic" and an "infidel," not to mention "Uncle Tom" and "sellout."