Despite much of the Southwest originally being Catholic in nature, religion in the desert can be a lot like flooding a basin. The isolation means the message gets spread to everybody, and there are not too many outside forces to compete with. That's the nature hydraulic empire--religions can be pretty uniform, easy to enforce, and prone to some very bizarre whims. In the Industrial Age, New Ange movements were informal and de-centralized, and hard to define vagaries. But in the new Middle Ages, most New Age believers were flushed out as heretics, and in the Southwest Hydraulic Emperors tightly guided from a grassroots belief system into a a highly organized and heiarchial one.
In a lot of ways, New Age is like Buddhism. There's a reverence for their Earth, a belief in enlightenment, and a need for purity and meditation. However, in other ways there are complete opposites. Buddhism focuses very much on the earthly surroundings of the natural world, while New Age focuses on the beyond. The clear skies and the somewhat barren landscape have led them to study stars and see them as sacred.
Astrology plays a large role in the religion. The Zodiac is the frame of reference for religious doctrines and practices. Priests are required to study the movement of the stars and planets. Both governor and peasant alike take their horoscopes very serious. Signs will often play a role in the name a child is given, and the career they are apprenticed towards. It's also a large part of matchmaking, as marriages between incompatible signs are a taboo. Many a tragic tale is told over "star-crossed lovers".
Priests have a very active role in the lives of the southwest populace and royal courts. Besides astrology, they are also trained to develop therapeutic teas and massage techniques. They are often charged with healing, which may sometimes rely on herbs, but just as often disease is countered with crystal baths and chanting. In funeral rites, they may place emeralds with departed.
There is a specific priest caste which religious higher ups are born to, but ever now and then they will learn of a child with strange or autistic behavior, who they will induct into their ranks. They are called Indigos, and their jobs usually involve calculating or deciphering mathematical equations, which the priests will interpret the meaning of.