I don't know, I was very foreigner and I stick out like a sore thumb (you could probably spot me from satellite photos in a busy street), and I had absolutely no issues finding rent, banking and all other services outside of obtuse language. Other English speakers I met around never had issues with it either, including other Asians and even people of color (who you'd think would be affected a lot, but Japan's actual racism is very targeted to their neighbors, not unlike everywhere else I've been at).

It seems to me nobody has any problem with you if you make a minimal attempt at speaking using Japanese (most of them don't understand English at all and that puts them "on the spot", and while you can find some who are adept at Spanish and Italian and other languages you'd never expect, by raw statistics you aren't going to meet one of those in the streets if you are asking for directions or something). They seem to be pretty reasonable about it if you suck or make mistakes, but they seem to really value the effort.

About the bars, I never pried too much, but I was told it was Yakuza hangouts and I probably don't want to go in there anyway. I don't think locals are welcomed either. Not sure if they were messing with me or not, but to be honest they didn't look like a place I would have fun into if I was magically accepted. None of the actually fun places seemed to have an issue having me or my colleagues as patrons.

I have far more people checking me out while shopping like if I was a shoplifter, giving me weird looks, troubling me with paperwork and rent, trying to charge me more in restaurants or shops, and generally making me feel unwelcomed when I am in Spain. And I was born there! (I did lose the accent and I don't look very "typical" so they think I'm British or American).