There are two potential sources of conflict between Parris and Proctor.
First, Proctor had an adulterous relationship with Parris' niece Abigail. This occured before the story opened, so we do not know how much Parris knows about the situation. This potential source of conflict seems justified for a normal father figure, however, Parris cares very little about children. Abigail may be the last of his thoughts.
Second, Proctor fails to attend church regularly and he fails to adhere to every Puritan ritual. Therefore, Parris finds Proctor less than an appropriate Christian. This continuing tension in their relationship shines through the text as Proctor criticizes Parris' preaching content and Parris criticizes Proctor's church attendance. The conflict between these two men demonstrates a difference regarding the practice of a faith.