Natsubaki-sama
This is Kawaguchi Hidetoshi. This is a humble answer to the question.
When it comes to religion, like Tetsuya Urakami, I believe that mutual respect and tolerance are really important.
Conflicts have arisen due to conflicts of ideology, principles, and religion, and humanity has repeated tragedies over and over again until now.
Even in Buddhism, conflicts with original indigenous religions, beliefs, and ideas in India and in various countries/regions caused various adverse effects, and of course blood sometimes flowed, and of course, each religion tried to expand its power by strengthening ties with the power of time, and of course, there were many disputes involved in that.
However, Buddhism originally taught immortality, immortality, innocence, and patience, and since there is a tendency not to like conflict or confrontation originally, they are determined to try to reconcile with indigenous religions, beliefs, and ideas without conflict, and conversely, incorporate them. For example, Brahmin Hinduism in India, Confucianism, Taoism, etc. in China and Korea, Bon religion in Tibet, and Shinto in Japan.
In terms of general trend, I think it can be said that confrontation will be avoided by worshiping each god or dignity that is the object of worship as the guardian deity and guardian deity of Buddhism. Among those gods and honors, there are many that have been exalted to beings such as King Myō, Bosatsu, and Nyorai.
Of course, I think it is necessary to pay attention to the fact that gods and honors that have been upgraded to Buddha and Bodhisattva do not exist as entities, but rather that each one is given a role as an expression of Buddha's teachings, and exists as help towards enlightenment, liberation, and nirvana, which is the purpose.
Based on the above, in my humble opinion, I know that even monks and Buddhists do not have any particular problems with visiting Uji or Chinju-jinja Shrine to pray for peace, safety, health, longevity, etc. on the premise that it is to proceed with Buddhist training.
I hope you find it at least a little helpful.
Kawaguchi Hidetoshi Gassho