The Irish aren't very racist and they don't care what your race is really.
However the caveat is that my experience is not representative of the whole immigrant experience in Ireland, some places may not be as welcoming as others. I suppose the general warm hospitality of the Irish to immigrants was partly because of the same struggles and discrimination that the Irish people themselves have endured from the British and in other countries so you guys understand.
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There's an area in Dublin centred around Parnell Street (and to a lesser extent Capel Street) that is home to a large Asian community (Chinese, Korean, Japanese and Vietnamese mainly) and it's quite popular for its restaurants and bars.
You'll largely be fine for being of Korean ethnicity.
Suffered for hundreds of years at the hands of an oppressor? People will give you more shit for being American, I'd say.
Be prepared for a lot of slagging about the election.