Timothy Furnish wrote an excellent article for the History News Network on Divide and Couquer in Islam. Furnish wrote a book on millennialism in Islam that I have used for one of my lectures on millennialism. He is one of the most knowledgeable and straightforward writers on Islam, and what little I know is partly thanks to him.
In the article, Furnish addresses the question of whether there are in fact any such persons as moderate Muslims. There are, and he gives examples, Isma’ilis, Alawis, Druze of Lebanon, Zaydis of Yemen, Alevis of Turkey and the Ibadis of Oman. Some call Sufis moderate, but since Furnish knows his millennialism, he knows that Sufism has a lot of latent revolutionary potential just waiting for the right trigger.
I found Furnish's essay fascinating, and I appreciate his understanding of the various sects that make up the Islamic world. However, I admit to being a little nonplussed by his suggestion that as a matter of foreign policy we could try to "do business" with these moderate Muslims. For one, they only comprise 7-8% of the Muslim population. For another, the vast majority of other Muslims seem to regard them as marginal and strange at best, and heretical at worst. It struck me as analogous as trying to deal with the Catholic Church by talking to Jehovah's Witnesses. In some places, the sects are ascendant, as in Syria, where the rulers are all Alawis, but in general these sects live on the margins of the Islamic world.