The second camp also invokes Muslim practices to claim modern political ideology meets the basic requirements of democracy. For example, it often points to the shura or advisory council, where ideas were debated before submitting proposals to the leader --as the equivalent of a parliament.
The third camp advocates ijtihad, or reinterpreting Islam to make it compatible with the universal concept of democracy. This position is more common among lay intellectuals than among clerics. But the opening up the doors of ijtihad, which conservative scholars had believed were closed in the Middle Ages, has already produced its own spectrum of ideas, not all in agreement.
The Islamist reformers often have a larger audience in the West than in their own countries -- and not just because of censorship and harassment. Some are deemed to be too intellectual, too abstract, or tied to an artificial theology. Their philosophical approach is disconnected from popular religious practices and the teachings at most madrasas, or religious schools.
The new Islamist brand will increasingly mix technocratic modernism and conservative values. The movements that have entered the political mainstream cannot now afford to turn their backs on multiparty politics for fear of alienating a significant portion of the electorate that wants stability and peace, not revolution.
But in countries undergoing transitions, the Islamists will face a tough balancing act. In Egypt, for example, the Muslim Brotherhood cannot cede its conviction that Islam is all-encompassing. Yet it risks losing popular support unless it can also reconcile Islam with good governance and human rights.
To do that, the Muslim Brothers may have to translate Islamic norms into more universal conservative values -- such as limiting the sale of alcohol in a manner more similar to Utah's rules than to Saudi laws, and promoting "family values" instead of imposing sharia norms on women.
Many Islamist movements still do not share the democratic culture of the uprisings. But given their own demographics and the wider constituency they seek, they will increasingly have to take into account the new political playing field created by the demonstrations -- even within their own movements.
The exercise of power can actually have a debilitating effect on ideological parties. And for all their recent political success, Islamists also face a set of constraints: They do not control the armed forces. Their societies are more educated and sophisticated in their worldviews, and more willing to actively express their opinions than in years past. Women are increasingly prominent players, a fact reflected in their growing numbers in universities.
Ironically, elected Islamists may face opposition from the clergy. Among Sunnis, Islamists usually do not control the religious institutions. Egypt's Muslim Brotherhood does not control Al Azhar University, the Islamic world's oldest educational institution dating back more than a millennium. The Brothers may have won a plurality in parliament, but none of them is authorized to say what is or is not Islamic without being challenged by a wide range of other religious actors, from clerics to university scholars.
The biggest constraint on Islamists, however, may be economic realities. Focusing simply on sharia will not spawn economic development, and could easily deter foreign investment and tourism. The labor force is outspoken and does not want to be forgotten, but economic globalization requires sensitivity to international pressures too. The newly elected Islamists face political rejection if they do not deliver the economic goods.
Israel is still unpopular and anti-Western xenophobia has visibly grown, but Islamist movements will need more than these old issuesto sustain their rise to power. The Arab uprisings have shifted the battle lines in the Middle East, and Islamists will find it harder to play on the Arab-Israeli conflict or tensions with the international community.
At the moment, the most dangerous divide is persistent tensions between Sunnis and Shiites. The differences are symbolized by deepening political fault lines between the Sunni religious monarchy in Saudi Arabia and Iran's Shiite theocracy, but they ripple across the region -- from the tiny archipelago of Bahrain to strategically located Syria.
Just as Islamism is redefining the region's politics, Islamic politics and sectarian differences are redefining its conflicts.