None of my ancestors was executed in the affair, but I have two who were accused and a sister of a third (and thus the parents of that one are also ancestors of mine), plus the sister of one of the accusers. Reading the accounts of at least those participants, what struck me is how far these were from being heresy trials. There were heresy trials among the Puritans, and they did ending up executing four Quakers and banishing a number of others, so it is not like they wouldn't involve themselves in such things. But Salem seemed to have none of that. Let me quote from the wiki on one of the accused, Rebecca Towne Nurse:
A public outcry greeted the accusations made against her, as she was considered to be a woman of very pious character, who lived in amity with her neighbours, and had a reputation for benevolence as well as piety: even her neighbor Sarah Holton, who had accused Rebecca of acting quite unreasonably in a quarrel over some trespassing pigs, later changed her mind and spoke in Rebecca's defence. Thirty-nine of the most prominent members of the community signed a petition on Nurse's behalf. At age 71, she was one of the oldest accused. The examining magistrates, John Hathorne and Jonathan Corwin, who normally regarded the guilt of the accused as self-evident, took a notably different attitude in Rebecca's case, as they also did in the case of her sister Mary Eastey. They told Rebecca openly that if she was innocent, they prayed that God would show her innocence, for "it is a sad thing to see church members accused". Hathorne was no doubt influenced by the fact that his sister Elizabeth Porter was a close friend of Rebecca, and one of her staunchest defenders.No one accused her of the slightest deviation in doctrine or of disruption of the church or of any lack of Christian behavior, save that there were strange events occurring that pointed to witchcraft. Spectral evidence was allowed in court, based on unusual beliefs of supernatural, or more properly extranatural phenomenon. Specifically, there were people who twitched, and believed witches were tormenting them. They came to focus on Rebecca specifically in time. She was acquitted, but the afflicted kept twitching, so she was tried again, convicted, and sentenced for execution. She was reprieved by the governor, but that was later rescinded.
Massachusetts Puritans get the reputation worldwide for being the evil ones, but witch trials were hugely more common in England, and more common still on the continent. They were not more common in specially religious areas - Salem was a seaport - but in areas where there was population turnover. I don't want to paint that too strongly, claiming that Salem wasn't really religious or really Puritan at all. That's not justifiable.
Religion and science were not competitors in the Middle Ages, but joined at the hip. They grew up together, as in alchemy. At the level of intellectuals, thinkers and experimenters were trying to figure out what the laws of the universe and the laws of nature were. At the popular level, superstitions became more common. To give it a modern perspective, people of my generation might remember the Foxfire books. Among the Appalachian skills and customs that were collected and remembered were medical solutions. For a cough one might bury a rag under a stump, and walk around it backwards seven times reciting the Lord's Prayer. Writing itself was considered rather magical, hence the relationship between the word "spell" in spell-casting, spelling, and go-spel "good news."
People not only looked at nature to see how it worked, but looked to nature for signs. If a deformed pig was born, it was a sign that the owner or other involved person had committed some sin - likely bestiality. I went into detail in my Wyrd and Providence series, specifically Part V, in 2010. Two quotes from that essay:
The story of Micah Rood (recently a movie, I just learned) is of an apple tree which bore fruit that had red globules in it – the belief was that the tree had changed from bearing normal white-fleshed fruit to blood-tainted as an announcement that Micah had murdered a peddlar and buried him there around 1700. Nature herself would accuse. Nature herself would demonstrate. The story is not from Appalachia, or Virginia, but Franklin, CT.and from CS Lewis's monumental English Literature in the Sixteenth Century, Excluding Drama:
Only an obstinate prejudice about this period could blind us to a certain change which comes over the merely literary texts as we pass from the Middle Ages to the sixteenth century. In medieval story there is, in one sense, plenty of “magic”. Merlin does this or that “by his subtilty”, Bercilak resumes his severed head. But all these passages have unmistakably the note of “faerie” about them. But in Spenser, Marlowe, Chapman, and Shakespeare the subject is treated quite differently. “He to his studie goes”; books are opened, terrible words pronounced, souls imperilled. The medieval author seems to write for a public to whom magic, like knight-errantry, is part of the furniture of romance: the Elizabethan, for a public who feel that it might be going on in the next street. [...] Neglect of this point has produced strange readings of The Tempest which is in reality [...] Shakespeare’s play on magia as Macbeth is his play on goeteiaI am not claiming that this wasn't religious sentiment run amok in New England. Central to their belief was a vivid picture of Satan operating in the world. The belief in Satan was stronger than the belief in God, it seems. That is clearly religious belief. Yet the whole sad mess looks as much like bad science as it does bad religion. Religiously, Rebecca Nurse passed with flying colors. But there was still twitching, and you know what that means. Nature doesn't lie.
The Puritans read in the Book of Nature as intently as the Bible, and as literally.
Update: Recognising the historical event as something other than a heresy trial reveals Arthur Miller's The Crucible as even farther off the mark than before. I have liked some of Miller, especially "After the Fall." I still quote from "A Memory of Two Mondays" at times. "Death of a Salesman" is a bit overrated, but it is well-written. Yet he is very much bound to his time and was a prisoner of his politics. "The Crucible" is still produced and assigned solely because people still think McCarthyism was worse than communism. Only two of the characters are all that compelling.