Did the witch really take the baby? Or was it imagined by the parents of the baby?
Yes, in the context of the film's world, the Puritans' idea of witches--and by extension, black magic and the devil--are "real." This is the central twist of The Witch, and why I found it so clever.
Throughout most of the film, undeniably supernatural events happen offscreen, in flashback, and/or witnessed only by a character in severe duress--e.g. the baby sacrifice, or the older brother's encounter with a witch after becoming lost in the woods. Outside of these episodes, we're drawn into the drama of a 17th Century New England Puritan family that's flawed, tight-knit and relatably human, descending into dire straights as their farm slowly fails and they deal with grief.
By playing on our expectations as a modern audience, the film leads us to believe that we're watching a story set in the historical world, detailing a family's fraying psychological state, when we're actually watching a film set in the 17th Century world as the Puritans believed it to be: the devil is an active and powerful participant in human affairs, witches haunt the dark forests, and God turns a blind eye on those who've committed any sin.