This is just a thought, but perhaps the Japanese are scared of Koreans and other East Asians because they could physically pretty much pass as Japanese, yet this contradicts the need to be able to identify them as foreign. Japanese seem to have no problems with a bunch of foreign students and businessmen living in their country, so I don't think it would be such a big stretch to have the culture be accepting of permanent foreign workers as well.
Let's say that postwar Japan gets allied with South Vietnam or something. In the 80s, Japan is doing really well but S. Vietnam is a failed state. Since Japanese support for Vietnam is seen as a patriotic/conservative stance (defense against Communism), immigration from that one country becomes acceptable for the Japanese (including the conservatives who would have otherwise opposed it) and popular for the Vietnamese, seeing that the two countries' gap in wealth and HDI is massive.
By 1990 you have over a million Vietnamese in Japan, a number which begins to stay relatively constant due to stability in Vietnam and a slowdown of the Japanese economic boom. Race relations suffer a bit in the mid and late 90s as the economy tanks, but by this point the immigrants are more or less seen as permanent, and most government officials and bodies accept this. Discrimination continues but the life in Japan is still better than it would be back home. Furthermore, the presence of this large, highly-urbanized minority brings about an increase of awareness among the Japanese majority, and they help push for immigrant rights into the 21st century.
In contrast to OTL, where the presence of foreigners is marginalized, TTL's Japan is forced into national dialogue about the issue and they ultimately move to accept that the immigrants are there to stay. I think this is the inevitable result of the above scenario, though I admit I do not know if the Japanese would ever let in that many immigrants in the first place or how bad race relations would be. I picked Vietnam because it is far away from Japan culturally speaking yet still barely on the other side of the Sinosphere, so there is a still an opportunity potential mutual understanding. I assumed that Japan might let in the immigrants due to Cold War relations (save the Vietnamese from Communism!) and because of the judgement that their booming economy could support it.