Nobody ever pays attention to what people actually say in these games, do they?

The Crusaders were once considered outsiders (or, more accurately, a threat to the Maester's power) back when they were the militia group the Crimson Blades. The Maesters eventually began to accuse the Crimson Blades of treason. Their founder, Lord Mi'hen, travelled to Bevelle (along the road that would later be named for his journey), and fought the charges. When he convinced the Maesters of the purpose and loyalty of the Crimson Blades, they were renamed The Crusaders and became an official part of the Yevon clergy.

In FFX, Maester Kinoc is the current head of the Crusaders. Yevon only excommunicated those Crusaders who took part in the operation, and only before the operation took place, more as a threat and attempted deterrent than anything else. Despite having been officially excommunicated, the Crusaders taking part in Operation Mi'hen were heartened by the presence of the Maesters, realizing that the people of Yevon didn't abandon them, even if the organization itself did.

Further, after the failure of the Operation, the excommunications were cancelled, and the survivors were accepted back.