The previous answer was quite thorough. I would only add that part of the reason that Hale does change is that he is forced to recognize the duplicity that exists within individual actions. What would drive Hale to such a point could be summed up in a line from Yeats' poem, "The Second Coming:"
the best lack all conviction/ while the worst are filled with passionate intensity.
For Hale, he cannot understand how individuals with so much passion can represent the very evil he is committed to stamping out of Salem and of the world. There is a singularity within Hale that is fundamentally challenged by the end of the play. For example, in Act II, when Hale visits the Proctor home, he is about to leave before Francis Nurse and Giles Corey bust in with the news that their wives have been arrested. Prior to leaving, Hale tells John and Elizabeth that the path to their salvation lies in showing deference to the church and Reverend Parris, attending it more often especially on the Sabbath, and having their last child baptized. In Hale's mind, there is a convergence with religious purity and the institution. He cannot fathom that there would be a disconnect. It is this same reasoning that compels him to investigate Martha Corey after Giles talks about her reading. Hale simply cannot see something wrong in an investigation as he believes it is being conducted by flatly religious people. Hale changes in that he is forced to understand that there might be a disconnect in the psyche of individuals. The most spiritual of people might not be the ones that are considered to be so and the ones who are considered to be so might not be. Hale struggles with this, as he breaks from the court and seeks to pursue a more "grass roots" approach to ridding the town of witches in his desire to extract confessions. It is for this reason that he seems to not want to understand Proctor's motivation at the end. If he does understand it and accept it, the result would be a fundamental shift in that idea that there is a duality or a complexity within human nature and that the singularity that has dominated his life is not evident in an intricate setting. It is here where Hale undergoes the greatest amount of change.