Shinto is an interesting religion, somewhat similar to Hinduism, in that there is no formal doctrine and structure to it. Instead, as the native religion of Japan, it arose as a grass-roots collection of traditions and deities that eventually became the Shinto tradition.
However, when Buddhism came to Japan, things changed. Buddhism was a well-organized religion with doctrine, meta-physics, training, practices, etc. The first six schools of Buddhism in Japan were all devoted to study and interpretation of complex Buddhist schools of thought.
Shinto was never able to compete against this, so it became a kind of “secondary” religion in Japan. Shinto kami were often interpreted as manifestations of well-known Buddhist deities and so on.
However, there were attempts to organize Shinto along Buddhist lines in order to protect and preserve its traditions. One of the most well-known, before the modern era, is a Shinto sect called “Yoshida Shinto” (吉田神道) or “Yuiitsu Shinto” (唯一神道) meaning “the one and only Shinto”. It was started by a priest named Yoshida Kanetomo (吉田兼倶 1435-1511), who’s family suffered great misfortune during the dreaded Onin War. In the aftermath of the war, Kanetomo was determined to revive Shinto teachings, and and according to the Japanese Wikipedia entry, he synthesized Shinto, Buddhist and Confucian teachings of the time.
Kanetomo explained the relationship between the three religions using the example of a tree:
- Buddhism was the blossoms.
- Confucianism was the leaves and branches.
- Shinto was the root and foundation.
In particular, Yoshida Shinto used elements of esoteric Buddhist practice but applied toward Shinto teachings and such.
Like most Shinto schools, it bases its teachings of core, ancient Japanese texts such as the Kojiki, Nihon Shoki, etc., but its interpretation of these texts had influences from Buddhism and Confucianism along with folks beliefs.
Today, the influence of Yoshida Shintoism is not very extensive, but Yoshida Jinja, the home shrine is still a venerable shrine within Japan, and otherwise pretty mainstream. The website mostly seems to talk about general Shinto services and practices.
Still, it seems like it was an interesting experiment, one of many that arose during late-medieval Japan, to reconcile Buddhism and Shinto in a way that asserted “native” Shinto religious sensibilities more.