Old Faith is a term that refers to the loose collection of animistic faiths and religions of Etéra, though at times it can imply inclusion of Tebríthan ones too.
Many subset of what is currently called Old Faith can be traced to ancient or even prehistorical systems of belief. As far as it is known, they do not have a shared origin in the past. Instead, the unification of different factions under a big tent was largely a response to the spread of Gésh. As time went by, clashing elements weakened, while compatible ones were strengthened and spread further by the network of mutual support. In a thousand years, it became the norm for distant members of Old Faith to be mostly on the same page regarding the major topics, and have the theological and philosophical toolkit for reconciling the differences in minor ones enough to get along.
All Old Faith branches are fundamentally animistic. Everything of significance has a spirit, and the spirit can subtly (or not-so-subtly, for the more chaotic phenomena) influence an object, and be influenced in return. Yes, science can explain and predict things, but Old Faith is largely a faith of the gaps. Attempts at such subtle influence tend to rely on the laws of sympathy, like calling to like, ritualism and similar practices.
An important tenet is the acceptance of the same entities having different aspects. For example, an adherent from Southern Wejít knows the spirit of the sun as a benevolent underdog watching over the people. He moves to a desert in tropical Eastern Nariyása and sees people trying to appease the all-seeing tyrant sun, and proceeds to ask how those practices are to be performed, taking them in stride. This is because he recognises the sun to have multiple aspects, and the southern Nariyása to have a better idea of the tropical aspect of sun. Sometimes regional differences can make the pantheon complicated, such as one denomination sees the ocean and the waves as a single entity, while another sees them as separate and venerates the ocean while trying to appease the waves; by now, such dualities, triunities and so on are taken in stride by most believers, even if they may be mind-boggling to non-adherents.
Animals (including hominids), according to the faith, have much more concrete spirits, also sometimes referred to as souls. There is no consensus on what exactly happens to them after death, but many denominations postulate that some sort of afterlife or reincarnation exists, though they usually lean towards being at least semi-agnostic on the matter. Throughout most denominations, the phrase "Gave one's soul to [natural element]" is an euphemism for death, with the element chosen depending on personal inclination of the deceased or the speaker (sky, wind, forest, ocean and ground are the more common ones).
Old Faith concerns itself relatively little with matters of objective and absolute right and wrong, and instead focuses more on 'what works' and how to 'get along' in the religious context. E.g. littering in the forest is bad because it would anger its spirit, but not because of breaking some cosmic law. Still, people of the Old Faith are wary of growing overconfident or dismissing the power of a spirit as incapable of harming them - they tend to repeat that nature wasn't always on the decline relative to the hominids in terms of power, and things may change once again.