I was raised a "christian methodist" but I'm something quite different now. You're not stuck with the tools you're raised with is my point. You can choose to at least understand other toolsets even if you don't use them or like them
As far as living in Japan... you'll *never* be integrated there, just like you'll never be integrated into Mexican or German society completely. But you *can* reach a pleasant accomodation. In Japan, you'll always be the amazing dancing bear (as a few friends who live there put it). You'll have to be happy hearing "you speak good japanese" or "o my, you can use chopsticks" or "it must be wonderful to live in a country now with four real seasons". Its a lot of fun if you don't let it get on your nerves, particularly if people don't realize you understand what they're saying on the bus
As per dating Japanese women (wait a moment as I prepare to insult a huge number of men in Japan) ... they're annoyed that many of the men are still mentally stuck in the 1950s. So dating could be a win for you. Marriage is different because if they choose to marry a non-citizen, well I invite you to read Peter Payne's experiences on the web. He runs j-list.com and has an email blog about living in Japan being married to a Japanese national.
Its complicated but can be done. From what he says, he encounters little more problems than my wife and I did as we dated here in the US back in the 1970s.
Usually we'd get nasty or astonished looks from visiting Japanese businessmen and occasionally some distant relative in my family might say something really stupid like "I hear they make really good wives" .. .after which my wife would subtly cut them to shreds with her heavy Texas accent.
But if you're persistent, good-natured, non-judgemental about different solutions to societal pressures, and persistent (yes, especially persistent) .... one could do reasonably well there.. even become a citizen.