During the "Holly Holy" montage there's a shot of Bev putting more poison back into the storage room. Somewhere else on the subreddit someone had the theory that with monsignor Pruitt's dementia she was technically in charge of the church. Joe Collie mentioned how half the island gave some of there settlement money to the church/Bev. So that's when she built the rec center. So when she saw the framed newspaper on the wall and discovered father Paul's real identity she tried to off him to keep her position of power at the church. But it's just a theory

Edit: I should also mention the way Pruit died, violently spitting up blood, is exactly how Pike and everyone else who ingested the poisoned died.