What message does "The Minister's Black Veil" convey?

"The Minister's Black Veil" conveys the idea that we are all sinful by nature, and yet we hide our sinful natures from one another in an attempt to portray ourselves as sinless.  In this way, we erect a figurative veil between ourselves and everyone else so that they may not see our sinfulness.  We even attempt to hide our sinfulness from God, to no avail.  Further, our insistence on hoarding our secret sins and hiding them from the world seriously injures our relationships because it means that we can never truly know or be known, fully, by anyone else.  Even the most loving partners exist with this veil between them.

When Mr. Hooper's fiancee, Elizabeth, confronts him with the rumors which are circulating about why he wears the veil, he says, 

"If I hide my face for sorrow, there is cause enough [...] and if I cover it for secret sin, what mortal might not do the same?"

With this question, Mr. Hooper admits that he has the weight of secret sin on his soul and that he knows every other human being to bear this weight as well, including Elizabeth.  Even on his deathbed, when others tremble at his unwillingness to remove the veil, he says,

"Tremble also at each other!  [....] When the friend shows his inmost heart to his friend; the lover to his best beloved; when man does not vainly shrink from the eye of his Creator, loathsomely treasuring up the secret of his sin; then deem me a monster, for the symbol beneath which I have lived, and die!  I look around me, and, lo! on every visage a Black Veil!"

With these lines, Mr. Hooper has been more open about the meaning of the black veil than he ever has been, publicly, before.  (He did reveal a great deal to Elizabeth alone.)  He insists that he is not a monster because he has worn this veil, and it is ironic that he has been shunned because of this physical symbol that means nothing on its own but only acquires meaning because of what it represents.  The veil is meant to symbolize the sinful monstrosity in each of us, our capacity for dissembling, and our desire to hide our true natures from each other and from God.  He sees a figuratively black veil on each face because every person does this; every person tries to hide their true natures.