Hale actually does change his mind throughout the course of the play. When Hale first comes to Salem, he is excited to put his skills to use. He has had experience with witchcraft and he's intent on finding and fixing the problem of witchcraft and thereby showcasing his skills. In the character description, Hale is anxious and determined.

Coming into Salem now, Reverend Hale conceives of himself much as a young doctor on his first call. His painfully acquired armory of symptoms, catchwords, and diagnostic procedures are now to be put to use at last.

However, after hearing testimony, all of the accusations, and the illogical proceedings and arguments of the court authorities, Hale begins to believe in John Proctor and he begins to suspect that there simply are no accounts of witchcraft in Salem; he increasingly believes that the girls (namely Abigail) are lying. At the end of Act Three, Hale denounces the court proceedings because he sees no evidence and no merit in the accusations. While Hale essentially washes his hands of the whole affair (wants no part in it), he doesn't use his authority and influence to really support John and openly challenge (rather than extricate himself) the court and the accusers. He doesn't fully act on what he comes to believe (that the accusations are false). But Hale certainly does change his mind over the course of the play.