As one of the most important offices in the caern, this isn't one to hand out idly. In fact, it's one of the highest roles a Theurge can aspire to in Garou society. Admittedly, the Master of the Rite doesn't oversee each and every rite performed within the caern's bawn but he is responsible for overseeing all the rites performed at the caern's heart, which certainly covers all the rites for each moot and other significant occasions.
Of course, the built-in job requirements weed out any applicants who are as yet too inexperienced. The Master of the Rite must know a /lot/ of rites, and should possess Rituals 5 as well (or else there'll be no Level Five rites performed in the caern). Comprehensive knowledge of spirits and how to deal with them is also vital. The Master of the Rite is responsible for keeping cordial relations with the local spirits; he should also be prepared for any demands a spirit might have in return for empowering a fetish. The sept doesn't strictly require that the Master of the Rite be a Crescent Moon, but any non-Theurge has a longer road to tread in order to prove his ability.
Because of the involved demands of the position, this is one of the offices that usually indicates a character's retirement from active play. The most probably exception is for very small septs, wherein the Master of the Rite may have to go on missions with his pack because there's just nobody else who stands a chance of success. Otherwise, although this position offers a multitude of roleplaying opportunities (particularly in the spirit world), it's just not suitable for group play.