In particular, the southeast region (Gyungsangdo - GSD) is the core of the right-wing, and the southwest region (Jeollado - JLD) is the core of the left-wing. I really cringe at using the words "right" and "left" here because South Korean politics doesn't neatly align with what many Westerners would think of when hearing those terms. But for lack of better terminology...
In any case, the earlier presidents (or quasi-dictators) hailed from GSD and overtly favoritized their home provinces in terms of economic development, etc. while leaving JLD less developed. This has led to resentments that reflect in politics that persist to this day.
Some would argue the rivalry goes back even further. Historical texts exist that describe animosity between the GSD and JLD regions back into the Joseon dynasty. Going back even further, the GSD and JLD regions were the rival and enemy kingdoms of Shilla and Baekje respectively, the former which eventually conquered the latter.
It used to be that it was even taboo to marry across GSD-JLD lines, but again, this mainly affects the older generations. Personally - while I am Korean-American, my family comes from GSD. My wife is from JLD. My dad is on the conservative spectrum in terms of Korean politics and I was initially worried what he would think when I introduced my then-girlfriend to my parents for the first time. Thankfully it was a total nothingburger and my now-wife and my parents get along absolutely fine.
Unfortunately I can't find it now though; it was very insightful.
The sentiment is not non-existent in Korea itself too though. In fact, in some discussions of recent military developments by the RoK (plans for a aircraft carrier, SLBMs, F-35 and/or KF-X fighters, etc.) it's often touted by these folks that they are just as meant to be pointed towards Japan as they are to North Korea or China.
It used to be Koreans wouldn’t date Japanese out of hate but with few exceptions not many would refuse to date someone because they are Japanese (as business people or exchange students of each other and so on)
In any case, it doesn’t make sense to be anti Japanese since they’re basically on the same team these days: democracies who aim to keep their economies vital in the face of competition as well as declining fertility rates and also who must contend with a regional hegemon.
Maybe the old shintoburi is still going strong though.