The Sooni Heretics are a group of pro-human Sooni moderates who have been exiled from Sooni space. They actively oppose the Zealots and helped form CNK.
The heretics were originally just moderates who didn't agree with the hardline policies of the zealots. They didn't have any organization and none of them would have considered themselves to be 'heretical'. However once the Archigos crashed and the Council declared anyone who tried to help a heretic, a group of these moderate Sooni joined the human crew. They used the Archigos to return to League space, declaring themselves to now be known as the 'Heretics'.
After returning to League space, the Heretics needed both a cover story, and an organization to help them achieve their goals. Working with Rhaenvaeh Canel, Nyana McKenzie and Alastair McKenzie convinced the League government to give them the Corona Noir Ki system used in the Archigos Experiments to the heretics. They formed the Corona Noir Ki Institute, and have since been using that to further Heretic goals.
The Heretics' primary goal is to prevent the Zealots from destroying Humanity. In addition they want to wrest control of the Council back, get themselves un-exiled, and move the Sooni people into a more honest, mutually beneficial relationship with Humanity.
The Heretics still believe the Overseers to be Gods, but they believe that attempting to interpret their teachings is trying to know the mind of gods and belies the point of faith. They hold to a much looser interpretation, assuming the Overseers left their children to fend for themselves because they knew it was time. Now the Sooni people must have faith and live as best as they can with what they've been taught.