In OTL the Tokugawa Shogunate in Japan persecuted Christian converts, killing huge numbers of them and driving a minority underground. Japanese subjects were required to have certificates of religious loyalty from state-controlled Buddhist temples.
But what if the Tokugawa Shoguns had decided that, rather than outlaw Christianity outright, to bring it under state control like the Japanese government seems to have done with Buddhism? Buddhism is a foreign faith as well, but the Japanese were able to "tame" it easily enough. The shoguns could set up their own pope and require all Japanese Christians (who would have been Catholic) to obey that one instead of the Roman pope.
Bonus points if you can make it so the first Japanese anti-pope is Cristóvão Ferreira, who Liam Neeson played in the film SILENCE. In OTL he was arrested and tortured to the point he converted to Buddhism, changed his name, and snitched on foreign priests and Japanese converts, then apparently reverted to Christianity and was tortured to death. It might be easier to break him and keep him broken if he doesn't have to renounce Christ, but just his allegiance to Rome.