Hi, I am not a frequent reader of this sub so I did not see this question when it first appeared, but the long and short of it is that you have to divide this into two responses.

Shinto shrines were directly run by the government during WW2. Shrine Shinto had no existence outside government sponsorship and was basically an agency of war propaganda.

There were independent Shinto-based movements which the government sometimes allowed to exist independently. Under the threat of persecution for decades, these groups also allied with the government during WW2 and were apologists for all kinds of atrocities within Japanese borders. Buddhist and Christian institutions generally had the same kind of response. They defended the government to the bitter end in 1945. Dissenters were rendered outcasts.

After WW2 it was really only the Protestant Christians that were interested in addressing wartime atrocity; this part of your question would be possible for me to answer in greater detail, if you want to repost and narrow it. Some independent Buddhist lay groups such as Soka Gakkai also took up the cause of peace, although they did not become as serious about reconciliation with Japan's neighbors as the Christians. The other religious groups basically dodged the issue until the 1990s, when foreigners raised it, and responses have varied. Many Buddhist sects today have become quietly conservative and anti-foreign.