In the Scarlet Letter, why does Hawthorne want to associate Hester Prynne with Anne Hutchinson?
Let us look at who Anne Hutchinson was and what she did to stand out in the mind of Hawthorne.
Like the character of Hester Prynne, Hutchinson was born in England. She came to America following the Puritan minister John Cotton and lived in the Massachusetts Bay Colony. Also like Hester, Hutchinson was a Puritan, except that she was a leader in the Antinomian movement. This group shook the religious foundations of the colony due to its "free grace" theology. In this theology, the main point is that religion should not be a legal mandate, but practiced at free will. There are more ramifications of this movement, but that is not what matters to this question.
The important thing here is that Anne Hutchinson, a charismatic, powerful, strong-willed, and progressive woman within the Puritan society, had the strength of character to stand by her beliefs, and courageously take a stand, even if it meant gaining enemies. Moreover, Hester's own progressive view of the world, love, womanhood, motherhood, and even life itself would have qualified her to be a follower of Hutchinson, herself.
Yet, had little Pearl never come to her from the spiritual world [...] she might have come down to us in history, hand in hand with Ann Hutchinson, as the foundress of a religious sect. She might, in one of her phases, have been a prophetess. She might, and not improbably would, have suffered death from the stern tribunals of the period, for attempting to undermine the foundations of the Puritan establishment. [...]Every thing was against her. The world was hostile.
Hester Prynne, when compared to Anne Hutchinson is essentially being singled out as someone of equal leverage and importance in her community. She certainly is someone who also shook the foundation upon which the colony was built. She even stood tall in front of everyone at the scaffold and looked at them straight in the eye despite her feelings of anxiety and fear.
Most importantly, Hester used her scarlet letter, not as a token of shame (except when she used it to scare people off to leave her alone), but to show everyone that their judgement and opinions render no value into her life. She made the scarlet letter herself, and created it to look flashy, glittery, and artistic. Even more dauntingly, Hester dressed up her "sin", Pearl, with vibrant, rich, and showy clothes that broke every Puritanical rule of humility. All of these things directly questioned the status quo, angered many "devout" Puritans, and made her the social pariah that she became.
All these factors mirror the tribulations in the life of Anne Hutchinson. It is clear that Hawthorne admired the woman and wanted his main character to reflect equal courage to face society under the situation that she was facing.
Anne Hutchinson was a woman who was hated by the Puritan establishment for her independence and refusal to back down and do what she was told. It was crucial for each Puritan to be able to read the Bible for him or herself and to interpret it individually; this was one of the most significant ways that Puritans sought to differentiate themselves from Catholics. However, for colonial Puritans, conformity was needed to help the community survive. The first governor of the Massachusetts Bay Colony, John Winthrop, felt that religious unity was the social glue they needed in order to succeed in the wilderness of New England. Hutchinson, however, felt that God had spoken to her directly and she preached the idea that one need only wait to hear personally from God to know that one was saved (going to heaven). This doctrine went against the idea that one had to strive, and to work hard, to win such grace, and thus it made her incredibly unpopular with Winthrop and other community leaders. Hutchinson was eventually banished for her refusal to discontinue preaching what she felt to be the truth.
In linking Hester Prynne to Hutchinson, Hawthorne associates her with a very strong, but extremely infamous woman who was also disavowed by the community. The community's treatment of Hutchinson and her family was as deplorable and self-serving as is their treatment and judgment of Hester. They make "self-constituted judges" of themselves, a behavior that is antithetical to their beliefs, and their lack of kindness or even mercy is abhorrent. To connect Hester with Hutchinson is to connect the injustice of the fictional woman's treatment with a real-life woman's story.