The empathy we feel for Jake is probably due not so much to his narrative unreliability as to the style in which Hemingway presents the narrative. Jake is burned out. Different elements of the story illustrate this, but perhaps what's most significant is his outward indifference, while inwardly seething (though not expressing it) over the situations in which he finds himself. He obviously hates and resents Robert Cohn, though there is no objective reason for his doing so. Thus, his depiction of Cohn is one aspect of his unreliability as a narrator, and it does serve to show Jake in a kind of self-victimized mode. At the same time all of the story, in spite of the tensions and the atmosphere of catastrophe looming at any moment, is narrated in a matter-of-fact way that suggests how deeply alienated Jake is. And this, in turn, causes the reader to bond with him, to empathize with him as a pathetic man, a victim.
Jake's dysfunctional personality is shown partly in the scene where he prays in church. All evidence is that he's an agnostic, but it appears that his indifference and emotional exhaustion are such that he feels he may as well pray as do anything else.
The figure of Lady Brett Ashley looms behind Jake's distorted view of the action he narrates. She's clearly his ideal, but he paradoxically demeans her by setting up her liaison with the young bullfighter. At the close of the story we're left with the unbearable sadness of the whole situation, and (hopefully) a universal sympathy for all the characters as Brett regrettfully tells Jake that they could have had a hell of a time.