My Coptic friends have told me that sometimes Muslims will come in secret to the monasteries in Egypt to deal with problems that would not be acceptable to address openly in their own Islamic communities (exorcism and whatnot). This jibes with what I have read, too (e.g., "Journey back to Eden" by Fr. Mark Gruber OSB, which also mentions house blessing/cleansing performed for a Muslim family after the father died), though I have to be honest and say that this idea makes me pretty uncomfortable (not because I don't want to help Muslims be free of the devil, but because inviting Islam into our holy places invites that same demonic force). So the idea of Muslims worshiping in a church...I don't know about the canons, but I do know it is not acceptable to me or any of the Orthodox people I have known (including several priests). Salpy is right that there are many situations in which there is no choice, but when there is a choice I hope it is isn't controversial to say that it should be a clear and consistent no. Let the worshipers of the false "god" of the false prophet Muhammad worship their blasphemy in their own places, as they have long forced us to worship the true God wherever we can find out of their sight. Christians of any kind have no stake in the continuation of Islam in any way, shape, or form. May Islam (not Muslims) die a terrible, terrible death befitting its terrible, terrible life.
Would that all Christians could be as strong as the Axumites who tore down the attempts at a mosque in their holy city, and responded to the interference of Islamic leaders in the matter by saying "sure, you can have a mosque in this city when we can have a church in Mecca." That got the point across!