What is meant by "Ahl al-Baghy" (people of rebellion), what is the reason for their designation as such, what are their most prominent worldly rulings, and what is their fate in the Hereafter?

Linguistically, 'baghy' (rebellion/transgression) means injustice and aggression, hence the term "rebellious faction" (al-fi'ah al-baghiyah).

Jurists add further restrictions to the linguistic definition. According to the Hanafis, rebels are: a group of Muslims who rise up against a just Imam based on an interpretation (ta’wil), without deeming permissible the shedding of Muslim blood or the enslavement of their offspring, and possessing a deterrent force and power.

According to the Shafi'is, they are: those who disobey a just Imam—even if he is oppressive—due to their conviction regarding the fulfillment of a right incumbent upon them, based on a corrupt interpretation (ta’wil fasid) whose corruption is not definitively established, but rather they believe it justifies their rebellion.

Fighting rebels is obligatory by the consensus of the Companions. They are neither disbelievers nor transgressors, because their opposition is based on an interpretation they believe to be permissible, even if they are mistaken in it. Their affair in the Hereafter is with Allah the Almighty.