Communism and, by extension, Socialism need to root out any system of belief which challenges their primacy within the culture that they exist in. Within these forms of government the state itself must become the religion that is worshiped by the citizens, if it is not then the questions that will be asked of the leaders will be unacceptably sharp as regards their conduct in leading the country. The leaders become little tin gods, which bend and break when their subjects examine them too closely.
There are and have been countries that are communist and religious in the past. However, it is hard for communism and religion to coincide. Many of the worst dictators that led communist countries could not have been compatible with religion because they wanted to be the religion of the people that they led.
I do not think that a communist state is necessarily incompatible with religion. It can be said that both believe in the same aspect of a community that all believe in the greater good of a principle. But I also do not think that they are necessarily the same. I think there are variables.
I do not believe communism is directly incompatible with religion. Communism can separate church and state just as well as other forms of government. People shouldn't assume that communism is automatically bad. Yes, it has been used and failed, but generally with bad regimens and with too much force. Americans have been brainwashed into thinking Communism is inherently bad and that simply isn't the truth.
There is little to nothing in communism that makes it completely incompatible with religion. The two groups can work together in a country as long as their goals are compatible or they stay out of each other's business. Communism and religion both have their own issues, but they can work in the same country together.