If the priest or other religious person sails for free, then everyone's cruise fare subsidizes them (i.e. we all pay for their inclusion). Just like part of our cruise fare pays for the other entertainment staff.
Disney does not have anyone onboard run the Friends of Bill W (or other ANON groups), they just set aside a room and time. Its self-run by the participants.
The mass is "self run" in the same manner. A priest, minister, or rabbi is a guest as well. At mass, other guests serve as readers and altar servers.
As for sailing free, no one has indicated that is the case. Even if it is on some occasions, others sail free when it fits Disney's needs or plans..."kids" in the past at times, actors, CMs running studies, and who knows who else. Others get discounts...active military (which is wonderful), Florida residents, occasionally Canadian citizens. Apparently travel agents receive deep discounts. It is Disney's decision.