It's worth noting that, until they took over (and well, even after--see Froese's The Plot to Kill God about religion under Soviet Communism, for example), Communism was widely seen as "un-Christian" in Christian majority countries. Jewish religious leaders also did not care for Communism (studies in Poland have found that Jews were overrepresented in the Communist leadership, but probably underrepresented among communist voters--see Kopstein and Wittenberg's "Who voted communist? Reconsidering the social bases of radicalism in interwar Poland").

It's also worth noting that this has not prevented Communist parties from being popular in Muslim-majority countries, just as it did not prevent Communist parties from being popular in Christian majority areas. These aren't my areas of specialty, but I've been told by colleagues who study the contemporary Arab World, for example, that in the 1930's and 1940's the two biggest mass political movements in the Arab World were the Muslim Brothers (strongest in Egypt) and the Communist Party (strongest in Iraq). While there are a lot of books and small articles about the Muslim Brotherhood during this period, it's harder to find good material on the Iraqi Communist Party because, at least according to one professor I had, "there's just one big, massive, seven hundred page book explaining the whole thing in detail".

The Arab World isn't the only place where communism was popular. Turkey in the late 1960's and 1970s had a wide range of Marxist parties, but were cracked down heavily in the 1971 and especially 1980 coups (mostly, if I remember correctly, the Turkish communist parties are related to Dev Genç, including eventually the Marxist "Kurdistan Workers' Party", more commonly known by its Kurdish language initials, the PKK (the largest Marxist party in Turkey is currently in an electoral alliance which is seen as the PKK's political wing; they get ~8-10% ).

In Muslim Southeast Asia, it looks for a moment like Communists might actually take over, though Communism was widely associated with the (non-Muslim) ethnic Chinese minorities in Malaysia and Indonesia. See, for example, the Malayan Emergency and Communist Party of Indonesia (I don't have a source for this, but Wiki claims it was the "largest non-ruling communist party in the world prior to being crushed in 1965 and banned the following year", after Suharto's takeover and the transition to the "New Order").