Why was Anne Hutchinson a threat to the colony?

The Massachusetts Bay colony did not tolerate unusual religious views. The colony was run by the dour John Winthrop (1588–1649). Church and state in the colony were not separated very well. Therefore, any threat to the established church was also a threat to the rulers themselves. Roger Williams, a charismatic minister, was banished in 1635.
Colonial-era women in the American colonies did not enjoy equal rights. Anne Hutchinson was a forceful, eloquent, and intelligent woman, so she was deemed to be even more dangerous than Williams. She held weekly prayer services that were very well attended, but her religious ideas were unorthodox. To the men who ran the colony, she was strident and insolent. Her unusual religious views—like those of Joan of Arc two hundred years before—represented a threat to the male-dominated status quo. Seventeenth-century women were supposed to be extremely subservient, so Hutchinson's fierce defense of her views did not win her any friends among the men who chose to banish her from the colony in 1638. In 1643, she and most of her children were killed in an Indian attack.
Hutchinson was a dual threat to the colony because she challenged the status quo in both religious matters and gender roles. As an outspoken and courageous woman, she posed a threat to the established subservient status of women in the colony.

The key to answering this question lies in considering the larger context from which Anne Hutchinson emerged in Puritanical New England, because Puritanism entailed a very strict approach to Christianity. The entire New England colonial project was ultimately an attempt to create a Godly society, away from the influence and oversight of the Church of England. As a result, the New England colonies were dominated by its ministry, and its internal rules and traditions were shaped by a very legalistic approach to Christianity. There was then a very strong theocratic element at the core of its social and political structures.
Hutchinson deviated from Puritan religious norms. She revolted against Puritan power structures, where moral authority and teaching were dictated by the ministers to the parishioners, by holding her own discussion groups concerning the teachings of the Bible. Furthermore, her status as a woman further upset Puritanical sensibilities, which were very male-dominated. Her beliefs were the source of much controversy, and resulted in her banishment from the colony.
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Anne Hutchinson's defiance of Puritan orthodoxy is primarily what made her a threat to those in charge of the Massachusetts Bay Colony. She preached what is called a "covenant of grace." Simply put, this means that one's spiritual condition has no bearing on one's outward behavior. An individual believer's salvation has nothing to do with the performance of good works; it comes about purely through the grace of God and nothing else.
Hutchinson and other advocates of what came to be known as Free Grace strongly criticized the Puritan ministers of the Colony for preaching what's called a "covenant of works." In other words, the ministers believed that, although salvation is purely in the gift of God, it is nonetheless possible to observe outward signs of salvation through righteous behavior or good works. To Anne Hutchinson, this was a distortion of Calvinist theology. She maintained that there was absolutely nothing that an individual believer could do to be saved, nothing that they could contribute to their own salvation.
Hutchinson's defiance of the prevailing Puritan orthodoxy made her a dangerous figure. The fact that she was a woman also made her a real and present threat to the stability of this rigidly patriarchal society. Furthermore, her claim that personal revelation was equivalent to the teachings of scripture was considered nothing short of blasphemy by the religious leadership of the Colony. As far as orthodox Puritans were concerned, the Bible had sole spiritual authority, taking precedence over the religious experiences of individuals.