I don't think the line between Shinto and Buddhism has been very clear in Japan, just as the line between Hinduism and Buddhism was never very clear in India.
For that matter, whenever any religion travels it is forced to either defeat or integrate its newest cultures. Religion can't take prisoners of war, it has to conquer by assimilation or destruction.
I don't have personal knowledge of this branch of Buddhism, but I've made use of a search engine to find these sources.
Syncretism of Shinto & Buddhism in Japan
Most in Japan may know Buddhism has something to do with controlling
lust and anger, and is associated with funerals and graves, while
Shinto involves venerating nature, and weddings. But many people have
trouble making theological distinctions between the two or even
telling a Buddhist temple from a Shinto shrine.
The internationalists in the Japanese court welcomed Buddhism. Others
saw it as a threat to the status quo, with Buddha nothing more than a
“jajin,” or devil.
Prince Shotoku (574-622) promoted Buddhism and it took hold. Still,
Japan would never see a full conversion away from its indigenous
religion, as occurred to a much greater extent across pagan Europe
with the introduction of Christianity. Rather, Japanese absorbed
Buddhism gradually, mixing it with local folk religions.
This process played out in the divine realm, too, with certain Shinto
gods coming to be seen as protectors of the Buddha. One was Hachiman,
the Shinto god of war, who legend has it aided the construction of the
Great Buddha statue in Nara during the Nara Period (710-784). This act
of kindness won him the name “Great Bodhisattva (Buddhist saint)
Hachiman” in 781.
Reflecting this meeting of religions, Hachiman was sometimes depicted
in sculptures as a very unwarlike Buddhist monk.
But what does the eighth century have to do with mixups over temples
and shrines now?
The syncretism, or weaving together of religions, would continue over
centuries as Japan went about absorbing Pure Land, Zen and other
Buddhist sects from China. Over time, cross-pollination between
Buddhism and Shinto would deepen in a process known as “shin-butsu
shugo” (Shinto-Buddhism coalescence), or less flatteringly as the
“shin-butsu konko” (Shinto-Buddhism jumble).
Much of the convergence amounted to Buddhism trying to make a mark on
the host culture. Buddhist monks felt certain Shinto divinities needed
salvation. So they chanted sutras in front of shrines that were the
gods’ sacred homes.
Meanwhile, temples started sprouting up next to Shinto shrines, to be
called “jingu-ji,” meaning “shrine-temples.” By the 16th century, such
mixing and matching had become official policy.
Kamis vs Butsus
In modern Japan, both Shintō and Buddhist practice among the common
folk has taken on the air of “this-worldly benefits” (concrete rewards
now; Genze Riyaku). To many Japanese, Shintō and Buddhist
faith is primarily involved with petitions and prayers for business
profits, the safety of the household, success on school entrance
exams, painless child birth, and other concrete rewards now, in this
life. Shintō deities are called KAMI, SHIN , JIN , SAMA , TENJIN
, GONGEN , and MYŌJIN to distinguish them from their Buddhist
counterparts. The latter are known as BUTSU and NYORAI (all
mean Buddha or Tathagata), BOSATSU (meaning Bodhisattva), TEN
(meaning Deva), MYŌ-Ō (meaning Luminescent Kings).