For Danforth, the truth of the accusations of witchcraft are only relevant as it reflects on the integrity of the court. In this way, Danforth's belief or disbelief in witchcraft itself is immaterial. He only cares about the integrity of the authority of the court.
Political authority and religious authority are one and the same in Salem, and Danforth upholds what he strongly believes is the unarguable truth.
Danforth initially refuses to accept any challenges to the veracity of claims of witchcraft in Act III. Anything that would undermine the validity of the guilty verdicts and the stature of the court is anathema to Danforth and his purposes. As long as there is no proof against the truth of the claims made by Abigail and the girls, the court's proceedings have integrity.
At one point, Danforth states that the court cannot entertain the possibility of reversing its judgements because some people have already been put to death after being convicted of practicing witchcraft.
He argues that it would reflect badly on the court if he released prisoners after executing a number of people accused of the same crimes—regardless of their innocence.
Danforth is not basing his argument here on the truth of the witchcraft accusations. To the contrary, he is suggesting that the question of the truth of the claims is not as important as the mandate to maintain the authority of the court.
Perhaps Danforth does believe that witchcraft is a real thing. This view prevails among the majority of the Puritan community at the time of the trials. Danforth certainly aligns himself with the majority, especially as he sees the majority as the source of his own authority.