It seems to me there are two possible protagonists in The Scarlet Letter. The most obvious answer is Hester, as it's she who connects all the other characters; however, Arthur is the character who undergoes significant change (both inside and out) from the beginning of the story to the end. I must also confess that social class as a theme is a bit strong to me in this novel. All the primary characters are Puritans (okay, Roger is a bit of a mix), and they all have relatively the same standing in town because they all supposedly have the same standing before God. The only one, again, who may be considered as being in a higher social stratumis probably Dimmesdale. He is seen as being on a different plane than literally everyone else in the novel. Because of this, no one is willing to believe his "confession" as he's dying on the platform at the end of the story. Also because of his elevated position, Arthur suffers a grave crisis of identity as he lives one life in front of the world and another before the mirror in his private prayer (or torture) closet.
No man for any considerable period can wear one face to himself and another to the multitude, without finally getting bewildered as to which may be the true. (p. 203)
This is exactly his inner turmoil, his spiritual crisis. Arthur Dimmesdale is the only one who has any real social status, and he's also the one who experiences a crisis of identity.