sin is defined as transgression of the law
The literal definition of sin is a religious term and means violating religious commandments said to have come from a god. I only use the word metaphorically as Dylan does here. Ophelia is devout and tries to avoid literal sin, but that has drained the life from her, and THAT is her (metaphorical) sin against herself and an authentic existence:
Ophelia, she's 'neath the window for her I feel so afraid
On her twenty-second birthday she already is an old maid
To her, death is quite romantic she wears an iron vest
Her profession's her religion, her
sin is her lifelessness
And though her eyes are fixed upon Noah's great rainbow
She spends her time peeking into Desolation Row
Poor Ophelia!
The consequence of sin is death.
Death is an inevitable consequence of being alive.
You will not escape death
Yes, I know. Neither will you.
Whether you care or not, might not be obvious until your time has come.
I can live with that. Actually, I live better for not caring about sin or hell or believing that my mind is continuously being read and me judged.
And if you're wrong, you'll never know that you devoted so many resources to a false belief including your time, your money, and your attention (gazing at "Noah's great rainbow").