"Should they not be sensitive to the fact that many people in that area have fond associations and is sacred to the memories of many people that were baptized or married or buried there?" the priest added.
The old church is currently set to be renovated into an Italian restaurant, with with Fr. McCafferty said he has "no problem."
"...but the screening of horror films in there is another matter entirely," he told Ireland's The Times.
The Exorcist (1973), based on William Peter Blatty's novel by the same name, is the horror movie famous for levitating beds, spinning heads and pea-green soup.
The book and film portray the demonic possession of a 12-year-old girl and her exorcism by two Catholic priests. Blatty said he drew inspiration from a 1949 Washington Post story about a Jesuit priest's successful exorcism of a 14-year-old boy in Mount Ranier, Maryland.
While the U.S. bishops have previously said that the film stands on "shaky ground" theologically, Catholic film critics have said that for the most part, it tries to portray a real exorcism as authentically as possible.
It won two Oscars in 1974 for best sound and best writing and is one of the 20 highest-grossing films of all time. After the film's release, interest in exorcism skyrocketed in pop culture, sparking a subgenre of films surrounding the topics of exorcism and spiritual warfare.
The other film to be shown, The Omen, is a 1976 British-American that tells the story of the son of an American diplomat who is marked with the sign of the Devil and is the Antichrist.
In 2006, attempts to film a remake of The Omen were disrupted on location in Croatia, with sets vandalized and burnt down. The producers blamed the Catholic Church for the disruptions, saying they had decried the film and sparked the outrage.
Catholic reviews of The Omen tend to urge caution, as the film can be seen as depicting evil in a victorious light.
Fr. Cafferty said he hasn't seen either film, though he is familiar with their controversial content.
"They are not the sort of films that I would choose to watch myself. People have told me about the films and I would have seen bits about The Exorcist – I just don't understand why anyone would like to see it in a church," he said.
A spokesperson for the film festival has defended the decision, saying that the abandoned church would enhance the audience's viewing experience, and cited that the church has been defunct for almost 40 years.