Shinto is the traditional religion of Japan.
As is normal with real-world situations, every single word (even “is”, “the”, and “of”) in that sentence is controversial, and potentially misleading, but it is still the best place to start.
I believe that Shinto is best thought of as a religion, but that word tends to create an inaccurate image. Shinto does not have a founder. It also does not really have sacred texts; the oldest collections of Shinto legends are eighth century, and almost nobody within Shinto believes that they are literally true, or should be analysed as a guide to daily life. They are still extremely important to Shinto, but their role is completely different from the role of the Bible or Qur’an. Further, Shinto is not, on the whole, very concerned with what happens to you after you die, nor with what its practitioners believe about the world. It also has little to say on ethics. You cannot really convert to Shinto, because it is not clear what that would involve. You can practise Shinto and Buddhism at the same time, and most Japanese do. In short, it is very little like a religion, if Christianity and Islam are your paradigm examples of religions. Indeed, nineteenth century Christian missionaries to Japan denied that Shinto was a religion, and convinced the Japanese government. This came back to bite them when the government made Shinto compulsory while upholding freedom of religion; if Shinto is not a religion, there is no contradiction here.
“Traditional” might also be misleading. Shinto does not claim a founder, so its age is not clear; there is plenty of room for disagreement over when religious practices in Japan can first be called “Shinto”. The earliest date that I have seen seriously defended is 10,000BCE, while the most recent is 1871. I don’t think either of those dates is at all plausible. Personally, I think Shinto began around the fifth century CE, in Japan’s Kofun period, and some fourth century practices can reasonably be called proto-Shinto. Thus, Shinto has around 1,500 years of history, which means that it originates in Japanese prehistory, albeit barely. Islam is younger, Christianity is older, and Hinduism is much older.
Shinto has also changed a great deal over the last 1,500 years. I call the practices “Shinto” for that whole period because there are enough continuities to make it helpful to use one name, but there have also been a lot of changes. Shinto begins at around the time when Buddhism came to Japan, so most of Shinto’s development has been in reaction to and as part of Buddhism. We find people building temples to help Shinto kami achieve nirvana very early, and for a thousand years most people believed that the kami were manifestations of Buddhas and Bodhisattvas, or vice versa. The influences of Daoism and Confucianism are also obvious, and some kami come from Hinduism. Even the rituals at Jingū in Ise, commonly regarded as the most sacred location in Shinto, have changed almost beyond recognition in the last few hundred years. Shinto is a living tradition, and, in my opinion, all the better for it.
“Traditional religion of Japan” is misleading, then, if it makes you think of a religion like Christianity that arose from purely Japanese sources and has persisted unchanged since the beginning of time. On the other hand, Shinto is a set of religious practices that have been handed down in Japan, created by the people from materials both local and imported without reference to an authoritative source. Thus, Shinto really is, in my opinion, the traditional religion of Japan.