What was the religion practiced by the townspeople?

Nathaniel Hawthorne's "Young Goodman Brown" is a short story published in 1835 and is one of the best-known of Hawthorne's pieces. The religion practiced by the townspeople and, eventually, by Goodman Brown himself is not necessarily a religion per se; rather, it is a disavowal of Christianity.
The story features a recently-married Goodman Brown, taking leave of his (aptly named) wife Faith, who is reluctant to see him go on an unnamed errand. The obliquely-described journey takes place at night, through a dark forest, with travel companions who are known to Goodman Brown. Some of these characters represent religious affiliations (e.g., Goody Cloyse, a former religious mentor of Brown's). Faith, too, appears in the woods. Goodman Brown, a heretofore pious community member, occasionally falters in his resolve to participate in the unnamed ritual. Referring to his mentor Goody Cloyse, Brown states,

Not another step will I budge on this errand. What if a wretched old woman do choose to go to the devil, when I thought she was going to Heaven! Is that any reason why I should quit my dear Faith, and go after her?

The night-time ritual, attended by so many townspeople, is a form of devil-worship; however, its culmination is left ambiguous by Hawthorne, as Goodman Brown wakes up and finds himself in the woods. It is proposed that Brown perhaps "only dreamed a wild dream of a witch-meeting." Whether in a dream or in reality, Goodman Brown declares, "Come, devil; for to thee is this world given." The story therein describes Goodman Brown raging among the pines "brandishing his staff with frenzied gestures... giving vent to an inspiration of horrid blasphemy."
The religion exhibited in Young Goodman Brown could, broadly speaking, be called witchcraft. Specifically, this "witch-meeting" takes the form of devil-worship, as the characters in the woods evoke and emulate the devil by carrying a staff. This devil-worship, however, is defined solely in counterpoint to the Christianity it rejects. This is made clear in the story's conclusion, in which the town minister preaching is declared "anathema," and Goodman Brown fears to himself "lest the roof should thunder down upon the gray blasphemer." Hawthorne's focus on "blasphemy" and on the devil reinforce the notion that the occult, town-wide religion is best defined as anti-Christianity.