It's like how there are still white supremacist websites in the US even when a black guy is their president. Sure, there is at least one online community who show extreme hatred toward people from the Southwest region (I wouldn't name it, but it should be obvious to anyone who's been following South Korean news for the past several years[1]), but they represent the social norms of South Korea about as much as Youtube comments do of America. (They also tend to show extreme hatred of women, the liberals, the poor, the disabled, and North Korea.)
Also anybody who talks about "a couple millenia old feud" between these regions don't know what they're talking about. Case in point: in 1963, Southeast(Gyeongsang)-based candidate Park Jung Hee won the presidential election[2] thanks to the votes of both Southeast and Southwest regions. (He then went on to foster the regional discrimination we're talking about to secure his political base, and died a dictator, but that's another story.)
Even when it comes to economic inequality, the much more serious problem is that between Seoul (and its neighbor regions) and everywhere else. It was another social problem president Roh Moo-Hyun (2003-2008) tried to solve (by building a new capital city that specializes on administration, like Washington DC), but the constitutional court killed the plan by basically inventing "customary constitution" out of thin air. He was also widely supported by the Democratic Party (or several other names the party assumed in Korea's hectic climate), largely based on the Southwest region, but he himself was from Busan, the biggest city in the Southeast. So, there.
As for why these "island slaves" are always found in the Southwest region, I think there's a much simpler explanation: that's where almost all islands are. Look at the map of South Korea. Not all coastlines are shaped alike.
[1] By the way, if you know the site, admitting "I visit that site" will be about as beneficial to your online reputation as saying that you support Westboro Baptist Church.
[2] http://en.wikipedia.org/wiki/South_Korean_presidential_elect...