Oh, I'm a very white American expat. I've been living here for twenty plus years – and will never go back.
Perhaps what you said was true before the 90's but not being accepted and welcome into the society isn't the norm now. Let's put a caveat on that.
If you live here and do not speak the language, you will not assimilate. Without understanding and speaking the language you will not be able to socialize. The people I've met who believe that Japan is a racist country are the people who expect Japan to bend its culture to suit them and speak English with/to them.
Since I learned the language I have never once been spoken to or treated unkindly or excluded. When I couldn't speak the language I often felt apart.
These days more and more Japanese abled Western people are on TV. There was even a woman who was cast in the lead of a major Japanese TV series a couple of years ago. Japan knows it needs foreign workers and they're laying the groundwork.
One more caveat: Generation snowflake. Oh, I hate these people. These pompous little shits who come here and expect everyone to bend over backword to their will – oh, and they want to educate, too.
"Oh, women are so mistreated here. You should...".
"Oh, you can't refuse me service, you have to work with me and my dictionary. I don't care if you have other customers...".
" Oh, what do you mean there's no vegetarian option? You have to accommodate me cry, cry, cry."
A few weeks ago I was coming home from the airport by bus. This 30-ish-year-old woman ran to the bus with two young kids in tow, banged on the door as the bus was pulling away and demanded to be seated. The bus driver stopped and put her luggage in the outdoor compartment and let her board. She claimed to get car sick and requested the people in the front move so that she and her kids could sit up front. No one moved and she had to sit herself and her kids in various empty seats loudly complaining the whole time about how rude Japanese are.
The point is, pay attention to what kind of people say X is Y.