I'm a Muslim/UK citizen and interested in coming to Korea to teach. I saw a recent article about Islam in Korea and was wondering how I might be looked upon.I assume by "recent", you mean THIS article (or this one) and if that's the case, I commend you on your reading of Korean papers before you make the leap.
There's some, but not an overwhelming amount of decent English info on Islam in Korea. Sure, you can read Wikipedia (which I found pretty interesting) or some other "Islam in Korea" pages, but other than a few snippets in the news, there isn't much on how you'd be treated here. I'll try my best.
Since Korea has a pretty high number of non-religious citizens and religious persecution is relatively low (although Islam has a tendency to be tied to terrorism in the minds of many Koreans), I think the best way to go about this is to highlight the fact that non-Korean Muslims here are viewed as very foreign. As I mentioned in a comment on Diffism, there are different categories of foreigners and each one typically carries a certain reputation or stereotype.
You can pretty much break it down like this: Caucasians (teachers, military, government, contractors, business-types and tourists); Asian non-Koreans (laborers, cooks, nannies, tourists and "entertainers"); and other. The "other" is where many western-Asian/Indian/black or otherwise dark-skinned people would be categorized because many Koreans aren't sure where to put them. True, there are hundreds of black teachers here and probably thousands of dark-skinned contractors, businessmen and skilled laborers working here, but the average Korean just doesn't know for sure.
For instance, if an Indian fellow was walking with a bunch of Korean businessmen at lunchtime, it would be assumed that he's involved with business in someway, but if he was alone, it's pretty unlikely that he would be considered to be part of the business crowd. Another good example of this on Korea Beat today. The police refused to believe that an Indian man could be a professor at a Korean university.
Since I don't know your race or ethnicity, I won't offer any simple race-relations tips, but if you were to wear an igal or a thawb, I can say for sure that you'd be given a few looks, yet I wouldn't expect anything worse than what you are used to in the West. Exposure is a huge part of tolerance and acceptance here and since the Korean Muslim population is very small (only a few mosques with 30,000-70,000 followers), the average Korean just doesn't have much experience to go on. You can largely avoid this if you live in Itaewon, but that might not be what you're looking for. I would suggest checking out the Seoul Central Mosque though.
The government is trying to promote closer ties as well. I think you'll be fine and might even find a nice little community to join if you felt so inclined.
September 26th, 2009: Korea Times reports on feuding going on within Korean Islamic groups over the misuse of donations.