The church acted as a neutral party for the grail war...at least it should...
With Kotomine Kirei becoming the master of Hassan of the Hundred Faces (Assassin) his father Kotomine Risei joined Tohsaka Tokiomi joined the Tohsaka party of the war.
Kirei, ordered to hide Assassin till they are needed, kept one of them always inside the church to protect his father.
Asako, one of the female personas, was used by Risei to satisfy his perverted needs.