Where I grew up in the flyover parts of the USA as a mixed race kid, my school had around 5 people in my year who weren't either white or black, and experienced some instances of hillbillies and old people complaining about me being there because I didn't blend in. Can't say that the community really made me feel integrated despite being born and raised there. Interestingly my close American friends generally tend to have a similar background.
In Japan if you're hoping to blend in as a Japanese person, that's a pipedream - you're not Japanese, you don't speak, look, act, or think like a Japanese person, and you probably never will. It's not the same as America where anyone can legitimately call themselves American. And that's fine if you ask me, Japanese people have every right to preserve and be proud of their unique heritage.
But people will treat you "as an equal" in day-to-day life so long as you at least try to assimilate (speak some Japanese, be generally polite). So long as you don't hold onto the belief that one day you will be Japanese, then you won't be bothered by the fact that you're different.
I lived in China for some time as well, and that was similar; my friends who have lived in India seem to feel the same way, and I suspect this is the case in any country with a dominant ethnicity or sufficiently distinct culture.
That said I do hear it's harder to climb corporate hierarchy as a foreigner, but it's not something I worry about since I just work for global/foreign companies rather than for Japanese ones. A legitimate concern for others who want to join the rat race, though (still amazed @patio11 subjected himself to that).
Guess it's a difference of values; I for one would easily take walkability over blending in with the crowd, but maybe that's because I never have experienced that even in the USA (and I lived in SF and spent time in NYC, and honestly I have had as much culture shock in those places as I did in Tokyo). I've come to see "equality" as a different thing than how Americans typically view it, and my particular circumstances allow me to navigate around the parts where I would hit a glass ceiling while enjoying the parts where I wouldn't.