Once you accept a recruit, they will be given the “Plumbology Member (Ruby Rank)” gameplay trait. For a recruit to become a member you can simply use the “Accept Recruit as Member of Plumbology” interaction whenever you wish, but it is more fun to start a “Cult Initiation Ceremony” found under social events. Recruits can “Request More Information about Plumbology” but don’t have many other cult interactions other than asking to be accepted as a member, which may or may not go well.
You will then be able to “Explain Ranking System” to your recruits or if you decide they are no longer recruit material, you can kick them out. If the other sim does not want to join (likely due to not knowing you well or not in a good mood) they will get a bit tense, but nothing will show up for your sim. The other sim will also gain the “Plumbology Recruit” gameplay trait. If you are successful in getting a sim to join the cult you will get a happy moodlet/buff and so will the other sim.
