Like when in the Soviet Union people who disagreed with the ideology or the system was diagnosed as mentally ill since you had to be mad to not wanting to live in the most enlightened and advanced society in history?I imagine Illuminism is less science and more Scientology-- taking scientific things like electricity, the atom bomb, and pop psychology but linking them together in ways that are more consistent with a particular pre-written narrative than to evolving understandings of empirical findings or the scholarly consensus on such. Hence Scientology's claim to understand the mind like no other discipline and its intense condemnation of psychologists and psychiatrists, life forms lower even than journalists Such secrecy also serves to discourage independent investigation and encourage relying on whatever info the higher-ups in the organization provides, which allows said higher-ups to build a hierarchy of varying access to secret information one needs to be "initiated" into. As a secret society that has only recently become a governing force, the Illuminist leadership should be well aware of this.
Illuminism maybe wouldn't be staking out an exclusive claim to scientific truth, but it would claim philosophical truth or logic itself as its unique preserve given the Enlightenment heritage. But when it comes to the mind, the line between literature, philosophy, and science is not always easy to draw. I'm sure can expect plenty of horrifying experiments on the brain, or really offensive statements about the mental fitness of people the Illuminists don't like.