The world in which Squad 13 lives in is identical to a cult because of the totalitarian government that controls the economy, arts, religion, education, and personal lives Of literally everyone who exists.
All cults need a specific cause to form, and in this case a global war against the Klaxosaurs that severally damages the agriculture and landscapes of the planet, and allowed APE to overthrow the leaders of individual Countries and form a single government that made APE the ultimate leaders. Papa, as the true leader of APE, has a cult of personality - he uses every means to portray himself ideally to the people as their savior and God to make them submissive and obedient to him at all costs. APE installs strict rules that are demanded to be followed without any complaining, such as no sex, no emotions, no individualism, and no crime or else they will face punishment in which the worst is potentially death. APE allows the immortal adults to live normally as they have fully conformed into their regime but APE keeps constant surveillance on the children, as they are still young enough to rebel and must be thoroughly educated to ensure they do not rebel against APE. APE installs purges (called punning) anyone who does not fully conform to their regime or fails to meet expectations and all evidence of their existences disappear. Other punishments to make sure followers of APE don’t shorten in numbers are brainwashing - changing their perspective that is deemed treason against APE. This not only includes changing their opinions but also their emotions and personalities that are more favorable towards APE.
The usage of children piloting FRANXX was not suggested by APE but discovered by scientists when developing weapons against the Klaxosaurs. However, it was a conventional means for APE to control the children. If the Immortal and infertile adults couldn’t pilot because they lost their necessary reproductive abilities, then the mortal and fertile children, who had no other place in the world, would fulfill that role. It is similar to the motto of the German Nazis of child soldiers - “ Obey or be punished.” For APE and the adults, they not only indoctrinated children at their most impressionable, but removed them from the influence of the outside world, such any information that would violate APE’s ideals.
The children, although thoroughly educated on what was expected of them (fighting and dying for Papa for the sake of peace), they were allowed to act like normal children in free time, such as playing with toys, associating with their peers, getting presents, and tell fairy tells. But once they reached adolescence, these activities changed. APE imposed military-like order on the children and trained young them in everything as soldiers. The children were essentially conscripted for suicide missions and if they died in combat, they were praised as honorable sacrifices but never memorialized. And training included hefty doses of propaganda that encouraged an almost religious devotion to Papa.