Consider a person. A combination of genetics and personal experience determine what that person is capable of doing, both the full scope of their potential abilities and the range of choices within which they act. A person interprets the world around them by means of complex sets of symbols which include language and sensory history and beliefs; that interpretation informs the person's actions within their capabilities. The complexity of some symbol sets requires graduated learning, such as in mathematics where arithmetic necessarily precedes algebra which necessarily precedes calculus, or as in a piece of music where themes and harmonies are first introduced and then developed.
Consider an organization. An organization has no goals or agendas or physical form, it only exists as a mental construct, a convenience of thought for grouping people and resources together. It is a symbol set. Although an organization has no goals, much like a hammer has no goals, it can be shaped by people to suit some purposes better than others, as a hammer is well-suited for driving nails and ill-suited for cutting shortbread.
Consider an organization created with the intent of causing some systemic change in the world. An organization can only effect change through the actions of people; more specifically, systemic change is only effected by people acting in different ways, making different choices, than they had been previously.
People can be influenced to choose differently by changing their capabilities, changing their environment, or changing the symbol sets by which they interpret their environment.
Changing a person's capabilities may be done directly, as in the case of surgery, or indirectly, as in the case of training. The former is beyond the scope of many organizations and won't be addressed here. The latter is an instance of changing a symbol set.
Changing a person's physical environment is causing change in the world, which is the issue being addressed and therefore not under consideration. Changing a person's mental environment is an instance of changing a symbol set.
Changing the symbol sets a person uses - knowledge, beliefs, values - can change the choices made and actions performed by that person. Symbol sets may be tailored to favor some choices and actions more than others. These symbol sets in particular may be of a type that require learning in stages, where preparatory work must be completed and symbols assimilated before further exposure is meaningful. In some cases, exposure to later stages before previous stages have been assimilated may introduce a flaw in the symbol set which cannot be repaired, as when a premature revealing of the climax of a dramatic work changes the viewpoint for the entire work and irrevocably alters the emotional impact.
I therefore believe that Mr. Jefferson's opinions on the need for secrecy in Weishaupt's Illuminati are incomplete:
The means he proposes to effect this improvement of human nature are "to enlighten men, to correct their morals and inspire them with benevolence". As Wishaupt [sic] lived under the tyranny of a despot and priests, he knew that caution was necessary, even in spreading information, and the principles of pure morality. He proposed, therefore, to lead the Free Masons to adopt this object, and to make the objects of their institution the diffusion of science and virtue. He proposed to initiate new members into his body by gradations proportioned to his fears of the thunderbolts of tyranny. This has given an air of mystery to his views, was the foundation of his banishment, the subversion of the Masonic Order, and is the color for the ravings against him of Robinson, Barruel, and Morse, whose real fears are that the craft would be endangered by the spreading of information, reason, and natural morality among men. This subject being new to me, I imagine that if it be so to you also, you may receive the same satisfaction in seeing, which I have had in forming the analysis of it; and I believe you will think with me that if Wishaupt had written here, where no secrecy is necessary in our endeavours to render men wise and virtuous, he would not have thought of any secret machinery for that purpose; as Godwin, if he had written in Germany, might probably also have thought secrecy and mysticism prudent.
Furthermore, given that people acquire symbol sets, and given that an organization is primarily a symbol set, and given that a person's symbol sets influence their choices, the process we call Initiation may be understood as a person internalizing an organization's symbol set such that they make choices and perform actions consistent with that symbol set.
In and of itself, that's not surprising, and is what might be expected from Initiation; however, the choices and actions made may be those for which the organization is well-suited rather than those for which the organization was intended. In that situation, the choices and actions promoted by the organization may have little in common with the organization's claims and purposes.
This, then, is the puzzle. If some symbol sets require both graduated learning and secrecy to achieve their effects, and if the environment of secrecy itself tends to subvert those effects, how can the symbol set be replicated effectively?