I feel so naive (or maybe I'm from a too liberal country); I don't think I've ever even thought about an Asian guy not wanting a long-term relationship with me, a white woman, specifically due to his parents' views or social pressure
I've spent longer periods of time in Japan and China (not in Korea, though) and dated some local men. It's obvious that there's still a lot of xenophobia in both countries (and people have their personal preferences as well of course), but whilst there were a lot of guys that didn't want to have anything to do with a white woman, there were a lot of guys that seemed to be interested in me specifically for being a blonde, pale, blue-eyed, liberal foreign girl. I didn't feel that I and my dates were specifically frowned upon when being seen in public together.
I've never seen race as a problem, personally, other than that cultural or language barriers may appear. I don't think I would get very well along with somebody who would let a race or group pressure to be too big of an issue in a relationship: I'm fairly independent and have a habit of doing what I see is the right thing to do even if it causes me to get bullied by a group that disagrees. I'm often attracted to those same traits in another person as well. I'm also romantic enough to believe that somebody might love another as a person, without letting shallow values to break a beautiful relationship.
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It's not the sinful, but the stupid who are our shame - Oscar Wilde