When the new Buddhist temple that moved to Gensōkyō is not part of your sect.

You think Byakuren knows of other Buddhist sects out there? Like, the one she's practicing is probably based on the Shingon school – but there are others out there, such as the rival Tendai school. Then there's the later Jōdo Shinshū school with the well-known Ikkō-ikki.

And that's just Mahayana. There are also Therevada in the south and Vajrayana in the west.