Anathema is the term used by the Dragon-Blooded and the Immaculate Order to refer to the forbidden Celestial Exalted; namely, the Solars and Lunars. Since the Immaculate Philosophy is at least informally accepted through the majority of Creation, such Celestial Exalted who are present in any major city are at risk for being identified as Anathema and hunted down.
According to history as taught by the Immaculate Order, the Anathema once ruled creation with an iron fist, and it was only when the Immaculate Dragons defeated them that the human race was freed from their demonic masters. Since the Shogunate, Celestial Exaltation has been interpreted as a form of possession. According to Immaculate Philosophy, once someone is possessed by an Anathematic Spirit, they become a demonic force and the original soul of the host is devoured, the only viable response is to exterminate the Anathema with the Wyld Hunt.
This doctrine is believed almost without question on the Blessed Isle. Although the people under Imperial domination in the Threshold are forced to pay lip service to the Immaculates, few Thresholders accept Immaculate doctrine without question. An individual's deeds are more likely to determine the reaction there.
Since the events surrounding the disappearance of the Scarlet Empress and the theft of the Jade Prison, the normal mechanisms for taking care of Anathema have been tangled up in the impending civil war in the Realm. While this means that Solars are now able to travel more freely than they could in a long time, the presence of Abyssal Exalted (as well as brutal Solar leaders like The Bull of the North) reinforces the Anathema-as-horror story. It is worth noting that the Anathema story has at least a grain of truth; the Great Curse does make the Exalted violent and unpredictable.