Enseiji Temple, located down a small side street in Hagi is an example of something that was once the norm but is now unusual, it is both a temple and a shrine on the same site.
It is home to the biggest stone lantern in the prefecture as well as a huge Tengu mask. It is famous for being the temple where Ito Hirobumi, Japans first Prime Minister, studied as a child. I did hear that his uncle was a priest here.
The reason given why the shrine and temple were not forced to seperate is that they were holding writings of an imperial princess from several centuries earlier. As stated it doesnt make sense, but they were not forced to separate.
The shrine is a Konpira, a branch of the famous one on Shikoku known for protection for sea journeys. The temple part is Shingon and the honzon is a Jizo. The temple was founded in the 13th Century, a long time before the castle town was built.