Not so much of a nanny state as what they considered societal norms of the day.
Looks like the first to be accused were the daughters of a minister. They had been playing some kind of fortune telling game and fell ill. It wasn’t the minister who accused them but the doctor who couldn’t explain their illness.
The upper echelon of the church tended to be among the most highly educated in those days. For instance, Cotton Mather experimented with variolation which was an early form of vaccination. He also did a lot of experimentation with cross pollination.
I was basing my comment on post #15 comment:
“It was a superstitious population using their superstitions as a convenient excuse to target neighbors for personal vendettas.”