>>are there inherently compatible bonds between Islam and
>>Communism not present between Christianity and Communism?
Based on my knowledge of both Islam and Communism, I would say no, not necessarily.
You are correct, however, that most states with majority Muslim populations are socialist.
I attribute it to the fact that most of these states were premodern in terms of culture, economic organization, and infrastructure. A point made by many historians is that socialism is a modernizing force that attempts to rationalize or manage the transition to a modern society.
The problem, as Friedrich Hayek argued, is that change can’t reliably be managed or rationalized. A reasonably free market allows decision-making to be decentralized, and so mistakes in judgment are corrected much more quickly than in a system of central planning.
Well, that kind of association is a stretch of generalisation. Look at South America, or even the former Soviet republics, including Russia. These were places where Communism originated, at the grassroots-level.
Besides, Saudi Arabia was quite anti-USSR.
Supporting or not supporting Communism boils down to the interests of the key authority in power, in the country in question.