The funny thing, of course, is that Christianity has a long history of endorsing various versions of a "divine right to kingship," including, prominently, in this very era. It would be fairly easily solved by a workaround such as: The Emperors may not have been of divine descent, but they were of divine endorsement, recasting the descent from the sun kami as being some kind of misremembered message from the angels of God. Basically, it would be recasting the Japanese monarchy as a version of the Davidic kingship for Japan instead of Israel. You could probably come up with some tortured explanation for how the Emperors actually descended from David, who was supposed to predate them by a few centuries, too, just to avoid the question of "Why did God choose two peoples?" and to tie into the obsession with the Ten Lost Tribes of Israel (they're totally the Japanese, guys!).
More broadly, even without something like this the Church's behavior around this time suggests that they would have been totally willing to endorse a divine right to rulership by the Emperor and the Shogun (more in the vein of "they were made kings, so they have a divine right to rule") had they tolerated Church activities in Japan (or, ideally, converted, but I don't think they would insist on that).
