During the dream at the beginning of the movie, Karen finds an envelope from Viviane with the phrase "Claviceps Purpurea Ergot." Claviceps purpurea is a type of ergot fungus that can grow in rye and has been known to cause hallucinations. An alternate read of the movie is that the demons aren't real, and instead are just hallucinations due to tainted church muffins. The only people who are confirmed to see demons are church members (Betty, Frankie) or people who are shown to have eaten the muffins (Karen).
The sword used by the cultists is a copy of the sword used in the film Conan the Barbarian.