CAIRO, Egypt - In this presidential campaign headquarters, in a second-floor apartment in the Cairo neighborhood of Garden City, young female volunteers in full veil work alongside women in colorful headscarfs and those with flowing, uncovered hair. All work side by side with young men as they scan video clips on their computers.

This may seem odd for the office of an Islamist candidate in the May 23-24 elections. But it symbolizes the appeal of the one candidate who seems capable of bridging the deepening divide between secular and devout Egyptians. His is the campaign I'm most interested in.

At a time when Arab upheavals are pushing one country after another toward Islamist rule, the independent and grandfatherly physician Abdel Moneim Aboul Fotouh wants to show that an Islamist president can be tolerant and inclusive.

Many non-Islamists are skeptical. But Aboul Fotouh's appeal for Egyptian unity - across ideology and sect - has won endorsement by prominent liberals, including the face of the Tahrir Square revolution, Google executive Wael Ghonim. To the astonishment of many, he has also won the backing of the ultraconservative, Salafist Nour Party.

His candidacy is a long shot, although he's one of four front-runners. He's short of funds. (He says he will accept only Egyptian donations, not Saudi or Gulf money.) But he has attracted tens of thousands of volunteers, and his big-tent approach makes him the most fascinating candidate to follow.

If populous Egypt adopts a "moderate" Islamist path - somewhat along the lines of tiny Tunisia or Turkey - it could provide some balance for the region. And it could show how democracy and Islam can find a way to coexist.

Of course, the skeptics note that until last year Aboul Fotouh was a leader of the intensely disciplined Muslim Brotherhood; in 2011, the Brotherhood expelled him.

Long banned from politics under the regime of Hosni Mubarak, the Brotherhood is now running its own candidate, Mohammed Morsi, via its new political-front group, the Freedom and Justice Party.

The Brotherhood's extensive grassroots organization, based on a network of social-service operations, won it nearly half the seats in parliament; this organization gives Morsi a good chance to beat Aboul Fotouh, along with the two leading secular candidates, former Prime Minister Ahmed Shafiq and ex-Foreign Minister Amr Moussa.

Aboul Fotouh's supporters include liberals who fear that the Brotherhood is drunk on power; they say Aboul Fotouh tried for years to reform the Brotherhood from within. "The reason he has so much credibility among liberals," says the noted human-rights campaigner Hossam Bahgat, "is that his discourse and program are unique - in emphasizing we must come together. I think he is genuine about his commitment to civil liberties."

And, I hear over and over from his backers, the doctor listens to what people have to say.

As I visit Aboul Fotouh's modest headquarters, his staff talk in similar language about his openness to dialogue. One close political adviser is female, a Marxist, and a political science professor at the American University of Cairo.

His media adviser, Ali El-Bahnasawy, a journalist and self-styled liberal, recalled how Aboul Fotouh visited Nobel Prize-winning author Naguib Mahfouz when "no one would dare" after hard-line Islamists had tried to kill the writer.

Aboul Fotouh also opposed the Brotherhood's 2007 attempt to ban women from running for president and to establish a clerical body that would rule on whether parliamentary laws were in accord with sharia.

Of course, one could ask why the ultraconservative Nour Party endorsed the good doctor. Can he straddle a support base ranging from Trotskyites to the heavily bearded devout?

Egyptian analysts say the Nour Party backed Aboul Fotouh in part because of rivalry with the Muslim Brotherhood. But, says Nour leader Ashaf Sabet Saad Eldin, now deputy speaker of parliament (who spoke to me in his elegant, high-ceilinged office as he fussed with his iPad): "The Nour Party wanted a candidate with support across Egypt because we really worried Egyptian society would split with very negative consequences."

In other words, the ultraorthodox Salafis (about whom I'll write more in another column) are also searching for a unifier. Is it possible that Aboul Fotouh can really unify an Egypt split by religion, ideology, and class?

Here is where we come to the hard part. Liberal Egyptian friends tell me they are shifting away from Aboul Fotouh because they feel he is waffling on his old, tolerant positions. They say he shifted his stance on women's rights, and the role of sharia law, in a historic presidential debate last week.

When I interviewed the doctor in November, he stressed the rights of women, noting that his wife and two of his daughters are doctors - the third is a dentist.

He insisted the controversial Article Two of Egypt's constitution - which says Egyptian laws must be in accord with "the principles of sharia" - was "fine" and didn't need changing. Salafis want to make that article more specific.

Aboul Fotouh also told me that "some ideas of Salafis worry me, but a better way to engage them is to involve them in society so gradually they will be more tolerant."

He added: "We hope to lead the Islamic world toward more tolerance." He added, "We'll not go toward Salafism, Wahabism [a reference to the untraconservative Saudi brand of Islam]."

The doctor's positions remain the same, his media adviser insists, handing me discs with clips recorded from the doctor's remarks that have been posted on YouTube.

All I can say for certain is that Aboul Fotouh's candidacy sums up what Egypt needs so badly: a leadership that embraces Muslims, Copts, rich, and poor, and tries to bring them together. Whether he will have the chance to prove he is that leader is up to Egypt's voters to decide.