How does the theme of social class relate to the identity and apply the protaganist of The Scarlet Letter?

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.

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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.