How does Hawthorne draw a connection between the Virgin Mary and Hester?

Hester sees her baby as a gift from God rather than a baby born out of sin. Pearl is the product of love and passion. Hester is willing to distance herself from Dimmesdale to protect her baby. Pearl comes to symbolize a wild divinity that God had given her.

Had there been a Papist among the crowd of Puritans, he might have seen in this beautiful woman, so picturesque in her attire and mien, and with the infant at her bosom, an object to remind him of the image of Divine Maternity which so many illustrious painters have vied with one another to represent; something which should remind him, indeed, but only by contrast, of that sacred image of sinless motherhood, whose infant was to redeem the world. Here, there was the taint of deepest sin in the most sacred quality of human life, working such effect, that the world was only the darker for this woman's beauty, and the more lost for the infant that she had borne.