Lunarians are a species that are remarkably similar to Humans, except with having a multitude of differences with them. Lunarians compared to the Humans, traditionally fear impurity, and also often have concepts of racism. As Lunarians cannot age or become sick upon the moon, as in, Lunarians are always of good health upon their home, the far side of the Moon. But should they be upon any location, to, or similar to Earth, (such as Gensoukyou), they would start to be exposed to sickness and death, which is what they avoid upon going through with. They are typically a Utopian race.
Not only the higher-ups of the Moon Rabbits, the Lunarians have also founded the Lunar Republic and The Lunar Defense Corps, and have put their civilization onto the far side of the moon cloaked and kept secret. Often sabotaging attempts of others trying to claim the Moon, as they view themselves as the first to be there, and the first to live there, therefore the Moon would be their's.
Lunarians are often highly pale due to living on the far side on the moon, meaning that they don't see a lot of sunlight at all, despite appearing like a normal human, and having hair colors of them, Lunarians also have possessed being able to have unnatural hair colors (As Yorihime and Eirin show), and possibly unnatural eye colors. Though overall, they just appear like a pale human who's seen no sunlight.
What Lunarians worship is unknown, but what is known is that Tsukuyomi is considered a Lunarian, and the Lunarians live under his de jure rule.
Otherwise, Lunarian culture is roughly akin to the days of feudal Japan--arguably Edo period, where there is one emperor/empress, and a shogun acting as a sort of governor. Despite this, however, the Emperor/Empress generally the one leading, whereas the shogunate don't have the actual control. Most of the codes and style of the military reflect that of the Edo period, although technology is said to be much more advanced. As a result, buildings are that much more different. The royal family would be one that holds the most power, although with recent upturns, such as the Lunar Rabbit rebellion/Lunar Wars, the sort of power has been slightly divided. Nonetheless, the Emperor/Empress had remained supreme commander of the military, although insistence of Lunar Rabbit rights had changed the outlook, as most had thought to flee the moon during the war.
The tradition and style has remained for centuries. However with current acting "Shogunate", now being referred to as Commander and as a member of a Royal Family - Yorihime, the rights have been granted to said Lunar Rabbits, although some may not recognize it or believe it as such..