At the most basic, they are initiates into a Lunar cult or its associates – including obvious things as the Red Goddess, the Seven Mothers, Hon-eel, Yara Aranis, and the Crimson Bat, but also in the Lunar Empire such cults as Yelm, Annilla, and Gorgorma (but those are generally not Lunar cults outside of the Lunar Empire). It also includes non Lunar Empire cults as the Red Mask secret society in Prax. It often includes Nysalor but not always.Most Lunars can speak New Pelorian, but within the Lunar Empire, most people can speak New Pelorian. A Dara Happan can be a Lunar, as can a Pelorian peasant or a Provincial tribesman. Many people in the Lunar Empire are Lunars, but not everyone. Except that just about everyone in the Heartlands offers at least a little worship to the Red Goddess and the Red Emperor. Most Lunars live in the Lunar Heartlands, which is the center of the religion, but there are many Lunars outside of the Lunar Empire. Some even oppose the Lunar Empire. In short, Lunar is not an ethno-religious category like Orlanthi or Malkioni – anyone can be a Lunar.
It is worth also thinking of the implications that the Red Emperor is the head of the Yelm cult BUT has also come from Pelorian peasant stock on more than one occasion. And Hon-eel was from a Pelorian peasant village in Doblian where she grew up without a father. But Jar-eel is from the most aristocratic Dara Happan lineage imaginable. All are Lunars. And in fact all members of the same family.