But, in the communist world, the government is God. In the Muslim world, one is forced worship Muhammand and the Koran. Islam's wars are fueled by hatred of other religions. Communism wars were against capitalism and freedom. Both Islam and communism are totalitarian. But, I wouldn't say the two are compatiable.
The common folk in many Islamic nations are also used to being RULED by an elite, and a corrupt one at that, so it's not as if they're going to have to conquer free nations and free people. They'll just use the more radical elements in that society to destroy our own. Again, look who the Marxists are supporting. And inciting.
"Compatible enough" to do business with one another. What they'll do with a bunch of religious primitives afterward is anyone's guess, but mine is that the corrupt rulers will simply be bribed and then the rulers will bribe the religious leaders in their turn. Then we'll probably hear a completely different tune from the imams about the joys of secular government.