The Heart of the Matter by Graham Greene, like many of Greene's works, invokes both common theological problems and those rather specific to the doctrines of the Roman Catholic Church.
The first religious issue raised in the novel is that of whether it is acceptable to commit a lesser evil to prevent a greater evil or bring to fruition something good. One can see that Scobie is making such choices in agreeing to borrow money from Yusef to finance his wife's vacation, and in his eventual decision to commit suicide.
The second religious issue Scobie struggles with is the prohibition against taking communion if one is not in a state of grace. Other issues where Scobie's own wishes conflict with his duty of obedience to the church are the prohibitions against divorce and suicide. Scobie's dilemmas raise a more fundamental question of whether all sins are equal. In other words, would divorce have been a better solution than suicide?
Another religious issue here is whether intention or act counts more in making moral judgments.