Monk is a mysophobe ("germaphobe") on the show. Howie Mandel, who plays Father in this episode, is a germaphobe in real life.
The tactics used by the cult members on the street ("Free Personality Test," promise of a better life, being "saved," being better prepared for "the end," etc.) and at their facility including the "death" of people only because they left the cult are eerily similar and in a few instances identical to the tactics used by the most famous real cult known as the Church of Scientology that uses the writings of its founder, L. Ron Hubbard, as its basis, also known as "Dianetics." The main difference is that anyone who leaves Scientology is, according to their "laws," is labeled as a Suppressive Person (SP), and there will be an attack on those people using many tactics to discredit them (via social media, websites, etc.) Or there may be some who contact places of employment or families to ruin their lives. To reach the various levels within the organization, members are required to take "multiple courses of their own design for each level that costs thousands of dollars per course. If a person doesn't have enough cash to pay for them, there are counselors onsite to help them attain new credit and max them out. At one time their tax-exempt status was revoked by the IRS but after they threatened to sue the IRS enough times to keep the IRS in court for decades to come, the IRS re-instated their tax-exempt status. Escaping the Scientology organization takes a heavy toll on people. This is why support groups have been established to help people transition back to a normal life in each city they have a presence in domestically and abroad.
Beyond the fact that Howie Mandel who is a germaphobe, the ironic part of this is that he of all people is trying to help Mr. Monk get beyond his fears of germs.
One of the main differences between the Siblings of the Sun and the Church of Scientology is that the cult in this episode references certain religious aspects including the singing of hymns. In contrast, the Church of Scientology cult doesn't believe in and recommends against any kind of organized religion, using legal arguments to deny those claims. For instance, they state people are free to worship as they please, but they also state that the time spent in worship for an organized religion means that is time not doing Scientology work. This puts those people who are not doing the work in violation of the "Billion Year Contract" that each member is required to sign and stick to. Violators of that contract will be punished as deemed appropriate by certain members who deal with violators.
When telling Mr. Monk about the "Father" by the park bench, Stottlemeyer warns Monk: "This guy Robert is a Svengali." Svengali is a character in the novel Trilby by George du Maurier. In the novel, Svengali seduces, dominates and exploits a young girl named Trilby, and makes her into a famous singer. This theme was later taken on by Gaston Leroux in The Phantom of the Opera. The word "svengali" has come to mean a person who, with evil intent, dominates, manipulates, and controls another.