[Mr. Mompellion] had only laughed and said that even Puritans should recall that pagans, too, are children of God and their stories part of His creation. (1.1.10)
Michael Mompellion is very unusual for a Puritan pastor. He has kinds words to say about non-Christians. He prefers being in nature to being in a church. He even opposes witch hunts. Knowing this, it's no wonder that Anna trusts his religious insights so devoutly. He's simply a solid dude.
Dark and light, dark and light, dark and light. That was how I had been taught to view the world. (2.3.25)
Although Anna isn't a Puritan, she was raised around enough of them to internalize their value system. They believe in absolute morality: the idea that there is only right and wrong, and nothing in between.
"How easy it is to feel the goodness of God on such a day!" he whispered. "Sometimes I wonder why we shut ourselves up in churches." (2.4.11)
Mompellion sees the natural world as a deeply spiritual place. As we'll later learn, this belief can be traced back to his former life as an outdoor laborer. That, of course, is an unusual background for a minister, which might explain Mompellion's generally unusual disposition.
According to Thy Word. Why were God's words always so harsh? (2.5.21)
As the plague decimates Eyam, Anna is gnawed by doubts about God. She can't understand how an infinitely loving deity would inflict so much suffering on the world.
He intoxicated us with his words, lifting and carrying us away into a strange ecstasy, taking each of us to that place where we kept our sweetest memories. (2.6.11)
Mompellion is quite the preacher, huh? He can give his parishioners a feeling of ecstasy amid the most difficult trial of their collective lives. With rhetorical skills like that, the dude could convince them to do anything. He could turn Taylor Swift fangirls into Kanyeholics with two sentences.
"It is a trial for us, I am sure of it. Because of His great love for us, He is giving us here an opportunity that He offers to very few upon this Earth." (2.6.14)
Mompellion sees the plague as a test sent by God, which makes it the villagers' duty to accept its reign of terror with open arms. Of course, staying put in Eyam has some practical benefits as well: it limits the spread of the disease. We doubt that ol' Mompellion is thinking about science, however.
Why, I wondered, did we [...] seek to put the Plague in unseen hands? Why should this thing be either a test of faith sent by God, or the evil workings of the Devil in the world? (2.12.23)
Anna's religious doubts grow as the plague worsens. Here, she questions the villagers' immediate assumption that the plague has been thrust upon them by some higher power. Why can't it just be seen as a natural phenomenon? By couching the plague in religion, the villagers are making themselves feel more helpless than they actually are.
[It] shocks me [...] that people here are so desperate [...] that they [...] pay their last mite for these worthless amulets. (2.12.9)
As the plague worsens, the villagers turn to superstition and witchcraft in a desperate attempt to save themselves. People will believe in any crazy thing when they're hopeless. Regardless, Mompellion is horrified to discover that his flock is turning away from God.
I do not believe in witchcraft nor spells, neither in incubus nor succubus nor familiar spirits. But I do believe in evil thoughts—and in madness. (2.13.82)
Anna's stepmother, Aphra, is responsible for the spread of pagan mysticism throughout Eyam. Anna might not give much credence to the actual belief system, but she rightfully sees it as an irrational expression of fear and pain in the face of unthinkable circumstances.
"I thought I spoke for God. My whole life, all I have done, all I have said, all I have felt, has been based upon a lie. Untrue in everything." (3.15.89)
Our brains get blown when Mompellion drops this bomb near the end of the novel, basically saying that he no longer believes in God after Elinor's death. He was able to rationalize suffering when it was somewhat separate from him, but now that it's hit close to home, he doesn't know how to deal.