From what I read the Moonies were contributors to Abe’s party and the shooter accused Abe of promoting “Moonieism”
Although Abe himself was a Shinto / Buddhist.
The Unification Church also owns the Washington Times. It’s safe to say that it’s typically well to the right of most churches.
https://en.wikipedia.org/wiki/The_Washington_Times
Would not be surprised if figures inside the church were donors to the LDP.