The Outremer Society is reenactment of the medieval crusades, and thus we portray mostly the times of peaceful occupation by the westerners. This allows the most interplay between eastern and western personas.
Islamic persona offers a wide range of characters from merchants to dervishes to saracen warriors and more. Some rumours that a secret society called the assassins live in the nearby mountains.
Remember, medieval reenactment is a form of acting so your Modern (real life) religion and ethnic origins have no effect on the character you are portraying so be as creative when choosing your persona as you wish. Just keep in mind the type of persona you want, and the wide range of options available.
Sources for Isamic reenactment
Clothing and Garb for Islamic Persona
Feasting in Islamic Tradition
A PDF file containing Ilamic Persona Articles
Lands that can be controled by Islamic persona (Costs to be worked out in Bezants and/or Capture)