With countries as homogenous as Japan and South Korea, I don't see racism having a statistically significant effect
Sexism is an issue in both cultures, but if that is a major factor why is Japan's fertility rate right between Spain and Finland?
Work culture in South Korea is certainly problematic, although I would again bring up Spain and Finland. I would also note Japan's work culture has had a massive shift over the past couple decades. The average Japanese worker works far fewer hours than the average American worker, and fewer than the OECD average. The '90s stereotypes about Japanese work culture are no longer true
Why would you want to have kids in South Korea‽
Here's a better question: Why would you want to have kids in North Korea?
The fertility rate in the north is more than double the South, but here's a more interesting fact: The birthrate in the North has been steadily declining for decades in almost lockstep with the South (note: there is a bit of wonkiness with a couple years in both data sources. Ignore the outliers), just at a slightly slower pace
I used this site to compare country pairs. With the Koreas you can see shared inflection points, such as in 1981, and a general trend line that looks the same
Then compare Russia and Ukraine. A much more volatile fertility rate. In 1986/1987, both countries share a local maximum, followed by a very sharp decline that continues until a local minimum right around 2000. We don't see this pattern with the others (although they all seem to follow the same trend)
Finally you have the US and Canada. Shared local maximum in 1990/1991, and again in 2008. Both closely follow each other in terms of fertility rate inflection points, but not at the some times as other pairs
Also of note: All the lowest fertility rate countries (South Korea, Taiwan, and China) are geographically near each other, with very similar primary industries - high-tech manufacturing
My hypothesis: The most important factor is environmental. Likely an air pollutant of some kind (maybe several kinds)
I don't have much evidence for this other than correlated fertility rates, but it's the only thing I can think of that fits the data