What impact does the Catholic religion have on the decision Jig is considering
In Ernest Hemingway's short story "Hills Like White Elephants," a couple is depicted discussing whether or not to have an abortion. Your question concerns religion, a topic that Hemingway does not reference. It seems that of all the factors into making this decision that Jig considers, the doctrines of the Catholic religion are not in this mix.
In my reading of the story, Jig would very much like to keep this baby. She tells "the man" that they can have it all. But her first priority is to do what it takes to keep the man she is talking to from walking away. And it seems that he desperately wants her to have the operation, so things can be "like they were before." He definitely does not want to settle down, to commit to raising a family, to live what many would consider a productive life. Although Jig seems to want to settle down, to have a family, she is willing to do whatever he wants, however reluctantly. In this respect, the couple chooses a sterile existence, one without purpose or meaning. They choose death over life. The couple is without spirituality; their decisions are not based on religious principles. Instead they seem to be hedonists, traveling about from hotel to hotel, drifting as so many of those of the "lost generation" that Hemingway so deftly depicted.
I have read the story many times. I don't see anything to suggest that Catholicism or any other religion have much to do with the situation, although they might both feel that having an abortion is morally wrong.