While I have read (and enjoyed) a number of Graham Greenes spy stories (what he called entertainments), I have never read any of his religious novels, including Brighton Rock. Therefore, I do not know how faithful the new adaptation of the film is to the novel. I also have not seen the 1947 film version. The current film is an effective gangster tale, but the religious elements (with one exception) are, I think mere decoration.
Pinkie Brown, a vicious thug, kills a member of a rival gang. He winds up wooing and marrying (so she cannot be compelled to testify against him) a young, innocent waitress, Rose, who has information that may lead the police to him. Both Pinkie and Rose are Roman Catholics. There is material here for an exploration of how sincerely held religious beliefs may not influence behavior, but the film does not deal with this matter in any serious way.
The exception I mentioned above is the ending. It is one of the most darkly and ironically comic endings I know of in film and literature. While it explicitly connects religion to illusion, I do not take this as any serious, general statement. The ending is merely a very clever contrivance providing grim amusement.
WARNING: I am about to give the ending away . . .
Earlier in the film, Pinkie and Rose pass a booth where one can make a recording. Pinkie, at Roses insistence, makes a recording while Rose stands outside the booth and so cannot hear what he says. He says that, while she wants him to say, I love you, in fact he hates her. At the end of the film, Pinkie is dead and Rose plays the recording. The needle gets stuck and so all she hears is Pinkie repeating, again and again, I love you. Then the camera pans to a cross on the wall.