Their religion has taught them that witches do exist, and they believe that it is possible for a witch to exist in their midst and for them to be unaware of her (or his) true identity and allegiance to the Devil. The Bible says, "Thou shalt not suffer a witch to live," and so they believe not only in the existence of witches but in their own religious obligation to root them out and hang them. These witches could, theoretically, be anywhere and anyone, regardless of how godly they might seem.
For example, Mrs. Putnam's grief over the loss of seven of her eight children compels her to look for a reason for their deaths. When she is unable to figure out some more practical reason that they died, she assumes that witches must be at fault. Reverend Parris chastises her for sending her daughter to conjure the spirits of the other dead children, but she cries, "I take it on my soul, but who else may surely tell us what person murdered my babies?" For her, and for many Salemites, it is a perfectly logical explanation to assume that witches (and the Devil they serve) could be the source of her misfortunes.