Well … this is a bit complicated, anonymous, because every region hosts a varied population, which means you’ll often see a wide variety of beliefs upheld among its people. While it’s true that many regions also have a regional religion tied to local legendaries, these are often only one of many possible, and in some cases, they’re not even the predominant religion of the region.
Take Kanto, for example. Contrary to popular belief, while it’s true that Kantonians generally believe that the legendary birds are actual embodiments of their respective elements, they don’t actually worship them. Rather, the legends tied to the birds are more or less folklore on the same level as local yokai. Instead, the predominant religion of Kanto is actually Shinto, with sizable percentages of the remaining population dedicated to Buddhism and Christianity. Only a small subset of people worship the legendaries themselves, and many of them place Mew at the center of their beliefs—hence the traditional name, Myuu-no-michi (Way of Mew). The beliefs upheld by the followers of Myuu-no-michi are often animistic in nature; that is, they essentially believe that peace can be found if a person becomes one with nature.
Johto, on the other hand, exists on the other end of the spectrum. While there are many followers of Shinto and Buddhism in Johto, it’s more common to find followers of Ho-oh, Lugia, or Celebi (or all three) there. This religion is commonly called Ubame-no-michi (Way of Ilex), although it’s also called Johtoism in Common. I could go into the finer details of what this religion means (I myself am a follower of the sect that worships all three legendaries and would be more than happy to elaborate on its teachings and traditions), but to simplify it as much as possible for the sake of this post, it borrows quite a bit from Shinto, including and especially the respect for kami (which are not necessarily just the legendaries but also the essences of nature in general). Johtonian belief states that all beings have their own essences, and thus, all beings have power and purpose, which in turn means that all living creatures should be respected. Of course, there are exceptions, but generally speaking, yes, Johtoism centers around respecting nature and doing as many good works as one can within their lifetime … or, essentially, it’s Shinto, except we also worship rainbow phoenixes, ocean birds, and/or woodland pixies. (We also believe that there are three beasts who will roam the world until humans are collectively ready as a species to receive Ho-oh again, and seeing as they’re still roaming, I feel completely at ease with referring to the major kami as “rainbow phoenixes, ocean birds, and/or woodland pixies.”)
Most other regional religions fall somewhere in between. Hoennians worship Kyogre, Groudon, and Rayquaza primarily, but their religion (Hoennism) follows the same basic tenets as Johtoism, just with the legends swapped out. (Contrary to popular belief, they do not worship the golems, the lati twins, or Jirachi; these are merely elements of their regional folklore.) By contrast, Unovans and Kaloseans, like Kantonians, don’t follow a regional religion. Rather, Christianity is the primary religion of Kalos (Catholicism, specifically), although I’ve been told more and more Kaloseans describe themselves as non-religious or Muslim. Judaism is also on the rise there as well. (And yes, a few also worship Xerneas, Yveltal, and Zygarde, but these people form a very small sliver of the population. Christians happened to be very charismatic people right around the Middle Ages, and in any case, the Kalosean religion somewhat lost favor thanks to the bit about a weapon devastating a large part of the pokémon population.) As for Unova, it’s more of a melting pot, so while a large number of Unovans describe themselves as Christian (Protestant, especially), practically every religion in the world is represented in some form or another there. However, there is no religion centering around its regional legendaries; this is merely folklore to the Unovans, not an actual faith.
Then, of course, you have the Alolans and the Sinnohans.
While Alola is just as much of a melting pot as Unova (although, as a place where many Johtonian and Kantonian immigrants have settled, it’s more common to see representations of Japanese religions there than western ones), there’s a hardy population of native islanders who worship the local Tapu. Like Johtoism, Alola is heavily focused on respecting nature, but for the Alolans, it has little to do with essences. Rather, nature itself is everything to them. It’s a powerful force in itself, yes, but it’s also a living entity that we humans are merely privileged to be a part of. As such, the local Alolan religion (it has no real name, as it’s tied heavily to Alolan culture) is steeped heavily in traditions, celebrations, and rituals that center around the respect and worship of nature, including its guardians, the Tapu.
Sinnohans, by contrast, follow a unique belief system that centers heavily on the worship of their entire pantheon. Every one of their legendaries is considered a deity to them, but this is especially true for Arceus (their main deity) as well as Palkia and Dialga (the gods of space and time, respectively). In a way, it can be thought of as a very western tradition in that the worship of the gods supersedes the worship of nature (whereas in religions like Johtoism, it’s the other way around), although that’s not to say that the Sinnohans disregard nature at all. It just means that a lot of their beliefs and traditions focus on acknowledging their gods as the creators of all existence and thus not merely a part of it but rather masters of it. (There are also followers of Shinto, Buddhism, and Christianity in the Sinnoh region, but honestly, they’re far fewer in number to the Sinnohans.)
Of course, this just describes the National Dex regions. There are many other regions out there with their own pantheons of legendaries (which themselves have varying degrees of importance to their people). Likewise, there are many other human-based religions out there, including Hinduism (one of the most worshipped religions in existence), Confucianism, Neopaganism, and so on and so forth. It all really goes to show how complex human existence really is. We each have our own ways of thinking and of living our lives, even within each individual region, and even if we share our world with such beings as Arceus, Palkia, and Giratina, we humans still have a lot of questions about who we are, where we came from, or what our purpose in this universe is—questions that we seek to answer through our vastly different faiths and belief systems. Or, well, through our inquisitive natures, of course.