Because yes, they have one. Possibly more than one.
We live in a culture massively dominated by one religion, and an unusually exclusionary one at that. This is less true than it was, and Christianity has never been the only religion in Western culture, but it has dominated the discourse for most of our history. That sometimes makes it hard to recognize religious practice as religious when it is very different from Christianity.
The presumed norm for religion–what most in our culture expect to see, even in a fictional religion–is something that resembles Christian religion (and, more broadly, the Indo-European and Semitic religions Christianity hybridizes), which is to say regular, frequent communal acts of worship guided by professional clergy and directed toward gods. But that’s not how all religion works in the real world! There are many possible models from different cultures–and in particular, religion works quite differently in the specific cultures Avatar the Last Airbender and The Legend of Korra draw much of their inspiration from.
For example, Buddhism has no gods. It has bodhisattvas, intercessory entities who are almost but not quite entirely unlike saints, but Buddhist practice consists of mindfulness, meditation, even prayer–but not worship as members of the Abrahamic religions or European pagan traditions understand it. Tibetan Buddhism, being part of the Theravada branch of the religion, doesn’t even have those; there are no higher beings on which one can call for aid at all, “higher” and “lower” being themselves illusions. The architecture and clothing of the Air Nomads draws heavily on Tibetan Buddhist monks and nuns, and Aang’s moral views (his vegetarianism, pacifism, pursuit of calm and detachment) seem drawn from the same source. It would not be farfetched to presume their religion is based on a similar model.
In the Earth Kingdom and Water Tribes, meanwhile (and one Fire Nation village), we find a veneration for local nature spirits. Disturbing the natural balance brings the wrath of the spirits, who must be calmed by an expert in such matters. This is not too dissimilar from practices in Shinto and Chinese folk religion, where all things–living, nonliving, and abstract–have souls, and disrespecting them can therefore make them angry. There is a real, qualitative difference between a Moon God and a Moon Spirit, namely that the Moon Spirit is the Moon, while a Moon God rules the Moon–in other words, there is not quite the same sense of hierarchy. The Moon Spirit is important and powerful because the Moon is important and powerful, but it is nonetheless not necessarily a higher order of being–setting it on fire hurts it just as it would you or I. One thus doesn’t need to worship Hei Bai to resolve its anger over the destruction of its forest; instead, one needs to understand it and persuade it to calm down by offering reparations and healing.
Just because there aren’t any gods in the Avatar universe doesn’t mean there isn’t religion. Unalaq is clearly a deeply devout man, recognizable as a religiously motivated tyrant just as Ozai is recognizable as a power-hungry tyrant–or if you prefer, recognizable as a religious zealot just as Amon is recognizable as a political zealot. Religion in the Avatar universe might not consist of regular meetings conducted by a priest, but it’s there–people know what spirits are, and tell stories of them. They know when they’ve done wrong and angered the spirits, and know that if they do, they need to find a sage, monk, nun, or Avatar to help them figure out how to appease the spirits. There are religious festivals–we see Unalaq complaining about how the Southern Water Tribe has secularized theirs. There are religious institutions–the Air Temples, the Fire Sages, the nunnery in “Bato of the Water Tribe.” There are sacred sites (spirit oases, the poles), rituals (meditation, the festival in Korra book 2), myths (the tug-of-war and love between Ocean and Moon, for example), religious art (the spirits didn’t build that bear statue in Hei Bai’s forest)–all the elements of religion are here. They’re just not arranged and presented in a way most of us are used to.