Droyne are communists. I mean this in the economic and not ideological sense; they are commune-ists. The oytrip (community) is closest in nature to the Jewish kibbutz.
Unlike human societies, Droyne make communism work because they are caste-based and inherently psionic. They are "wired" to be communal, and do not function well unless all castes are present. This means that they lack concepts of selfishness and (excepting Leaders and Sports) ego. In other words, Droyne communism works because they are alien.
Droyne do not have a religion. They have a philosophical doctrine of morality, of which the closest human analog is Buddhism, with Yaskoydray (Grandfather) occupying the role of Buddha. Whether or not they believe in reincarnation of the soul (or a psionic version thereof) has yet to be determined.
All Droyne mathematics are Base 6. This caused initial confusion among Imperial researchers, as Droyne have 8 fingers, until the link between Coyns and the caste system was discovered. As there are six Droyne castes, a heximal system of counting makes perfect sense. Young Droyne are taught to count only using their fingers and not their thumbs.
Similarly, there are 36 letters in Oynprith, the Droyne language. (6x6=36)
While Dryone understand the concept of uncasted things easily enough (nonliving things, animals, plants, and immature children all fit), they struggle with the concept that adult sentient beings do not fit into rigid, easy to understand molds. Therefore, aliens are terrifyingly random to the lower castes and are often baffling to Leaders and Sports. While the easiest way to explain aliens to other Droyne is to compare them to "a race of nothing but Sports," 1) this is still quite horrifying to them ("How do they get anything done?") and 2) deeply disturbing when they see an individual who nominally occupies a caste role suddenly act outside his parameters -- such as when a Marine (Warrior caste) is in charge of medics (Drone caste) and signal corps (Technician caste).
It is rumored that one of the reasons Sports are adapted to being away from home is to prevent lower caste Droyne from gibbering in terrified confusion at such chaotic beings.
Because this rigid social hierarchy is written into their genes, Droyne are an intensely law-abiding society. (In D&D terms, they are perfect Lawful Neutral.) This gives them an abiding love for both procedure and ritual: checklists, flowcharts and specialized tools are near and dear to their hearts. Both the Japanese Tea Ceremony and the ritual preparation of absinthe are aspects of human culture that the Droyne are able to fully appreciate.
Despite this, however, they find regulatory bureaucracy to be useless. ("Why use all these forms when everything would work more smoothly with a Drone reporting to a Leader?")
There are also some secret facts about Droyne which I shan't post because my players are reading this...