A Heretic is a problem for all religions, a jerk who twists words and shares their own ideas to lead fellows astray. Each turn, a Heretic will attempt to bring local Dominion towards 0, directly after Preachers preach and Temples spread the faith.
The Heretic trait has a point value, typically 2. Multiply it by 20%; that's the chance that the Heretic will reduce local Dominion by 1 each turn. Each Heretic does their work independently. If a Heretic trait is somehow 6 or higher, the 100%'s are lobbed off as guaranteed Dominion-reductions.
Insane Commanders and Shattered Souls sometimes engage in Heretical activities. This is actually a lesser form of regular preaching, however; it's in favor of R'lyeh for the insane, or Ermor for the shattered.