Were the political and religious authorities of Massachusetts Bay determined to get rid of Hutchinson or was Hutchinson a threat to the colony?

These two options are not mutually exclusive.  They are
both true.

The political and religious authorities were
determined to get rid of Anne Hutchinson, but they were determined to do so because they
felt that she was a true threat to the colony.  The Puritans of the Bay Colony believed
that God had made what was called the "national covenant" with them.  According to this
covenant, their community would be punished if they allowed "wrong" beliefs and
behaviors to persist there.

Because they believed this, a
dissenter like Hutchinson would have been seen as a real danger.  They would have felt
that they would risk God's wrath if they allowed her to stay.  Therefore, they were
determined to get rid of her because they believed she was a
threat.