Genuine question: why are native religions closed while European and Asian religions are open?
Native religions are closed because our culture, religions, and spiritual practices have been criminalized, erased, stolen, and bastardized by colonizers and continue to be today.
Many of us don't know our own traditions because they were beaten out of our grandparents and parents. Many of our traditions are lost forever because our spiritual leaders were murdered and their records were destroyed. Even many of the traditions that are still being practiced are struggling because of habitat destruction taking away vital resources (such as white sage and sweetgrass) and sacred sites. For the latter, the vast majority of sites necessary to different rituals and traditions are closed off to their tribes or destroyed entirely.
There's also other aspects to loss of spirituality in Native communities, like the fact that we have generations of Natives who were forcefully converted to Christianity, through schools or forced adoptions or predatory missionaries.
There's also just general loss. So many traditions were centered around things that many of us no longer have access to, because of laws or environmental destruction or removal from ancestral lands. How are we supposed to practice traditions centered around following bison, catching salmon, collecting maple sap, hunting water fowl, harvesting manoomin, building seasonal shelters, or the millions of other things that were stolen from so many of us?
Our traditions are closed because we still don't have real access to them, because they're still in pieces because of what colonization has done to us, and because they're STILL being destroyed by people stealing our sacred practices and turning them into something they're not, turning them into meaningless commodities.
To answer the latter part of your question, there's plenty of European and Asian traditions that are closed?? In my experience, "open" European religions are reconstructions, modern versions of ancient religions that no longer have a living community who follows them so there's no one being exploited by them being open. There's other traditions that are closed, many of them folk religions that exist in specific areas.
And in my experience, the VAST majority of Asian religions are also closed, with some rare exceptions like Shinto, or are semi-closed and require conversion or marrying into the community. If you are using "Asian religions" to refer to Abrahamic religions, then saying that they're all open is also not accurate. Judaism and many forms of Christianity are semi-closed and require initiation (conversion, baptism, etc) and there's at least one Abrahamic religion, Zoroastrianism, which is closed entirely.
In general, most religions in the world seem to be closed or semi-closed because they're based around dedication or culture, the former which you have to prove to the community and the latter you have to actually be part of to understand the context and meaning of the religion. The idea that religion is something you can just walk into easy peasy is very much an American Christian one, designed to convert as many people as possible as fast as possible. It's definitely not a universal concept.