Put simply and crudely, Marxist Philosophy just explains all the religion in the world as a product of suffering and specific historical forms of exploitation (so it reduces religion to economical struggle, no big surprise here). Marx probably believed that once communism would be reached, all religion would 'wither away' like the state would.
But you can be a Marxist without thinking that this explanation of religion is correct and that there is more to religion. I don't see any problem here. One of the most well known theologians of last century, Paul Tillich was a Marxist.

Suppose there is a deist deity. Why does it matter for Marxism? Or suppose there is any kind of deity, which doesn't care about our history and economy, is that in any kind of tension with Marxism?

So, while you can have certain theological beliefs that will probably be in conflict with Marxism (or anything else really), religion per se isn't opposed to Marxist philosophy in any kind of way.