Aha! If the boy was the most severely afflicted, perhaps the local school is a source? That would explain why the headmaster seems so eager to get rid of the shrine. And I suppose he'll never willingly let them perform a harae at the school.

Maybe they should just wage a purification war on their own turf? The protesters certainly seem willing to mill around there and disrupt their ceremonies, so they should be easy enough to catch. And they're probably crawling with kegare.