Admittedly, what got me first considering the possibility of a Christian Japan was an Otomo campaign I'd finished in Shogun 2 Total War, so I really don't know all or even most of the ins and outs of feudal Japan either. But the Catholics have a successful record of assimilating the practices of other religions into their Christian framework in order to smooth over the proselytization process, and the Jesuits in particular seemed good at this during the age of exploration. They had some success spreading the faith in both China and Japan before events outside their control (the Pope's ruling against them in the Chinese rites controversy and the rise of staunchly anti-Christian successors to Nobunaga, respectively) happened to derail the progress they'd made.
Perhaps if a Catholic or Catholic-friendly daimyo, such as said Otomo clan or Oda Nobunaga, had decisively prevailed over all comers and consolidated power at the end of the Sengoku period, they could've pulled it off in conjunction with a slightly more accommodationist Catholic hierarchy (tall order during the Counter-Reformation, I know). It's a little outside the original scope of this thread: but I think it'd be interesting if the Catholic Church in Japan ended up venerating Saint Amaterasu, blessed-but-totally-not-divine progenitor of the ruling dynasty, or something along those lines.