Hi there. I'm from Taiwan, and I have two younger sisters living in London. Next month, they're both going to marry Caucasian British men.
At first, my parents were against the idea of them dating Westerners. So was I, for a while. There were several reasons for this:
1. There's no use beating about the bush, part of it's down to simple racism. We are uncomfortable with the idea of our daughters and sisters marrying men of other races, because we felt it was weird. Unnatural. Disconcerting. This was despite our having lived in the US and the UK for many years, and on the whole having absolutely no problem coexisting with other races. White, black, Hispanic, Middle Eastern etc, we were okay hanging out with all of them. But when it came to love and marriage, suddenly it hit too close to home. It felt odd.
2. Part of it was due to my parents not wanting to marry their daughters off to a faraway land. You say you have traditional parents, so I'm guessing you're familiar with the popular Asian concept of "losing" a daughter when she gets married. The daughter is seen as part of the husband's family now. This is reflected in parts of the traditional Chinese marriage ceremony, as well as cultural norms such as the expectation that the bride would move in with the husband's family. My parents were uncomfortable with the idea of both of their daughters moving to London and staying there permanently, instead of marrying in Taiwan and thus staying (relatively) close to home.
3. In addition to the physical distance, marrying a Westerner would also cause other distances. There's the language barrier, for example. Very few people in our extended family speak English. There's the cultural barrier, never knowing whether what you're doing would be considered offensive to these strange foreigners. There are differences in protocol, in etiquette, in political and religious alignments, and in basic mentalities to almost every imaginable situation. These people are just so different, and marrying them just seems like a huge hassle.
4. This is sort of an extension of points 1 and 3 above. There's a slight cultural stigma in Taiwan regarding Taiwanese girls marrying foreigners. Taiwanese society, on the whole, is still relatively isolated, monocultural, and xenophobic. Girls who date Westerners are seen as fashion-chasing hussies, sleeping around with Caucasian men just because it's the cool thing to do. There's also a feeling of, "What, your own race isn't good enough for you? You snob." How much of these perceptions are based in reality is debatable, but undoubtedly it's unfair to paint all of these girls as phonies just out for a thrill.
Now, I don't know the details of your situation, and I'm not trying to pry, so I can only share my experiences and give you some general advice. For the first issue, it eventually took time. My parents and I got to know these guys better, and eventually accepted them as individuals rather than faceless Caucasian men. They both have their own strengths, weaknesses, personal quirks. My elder sister's marrying a guy with a bit of British noble blood in him. On the whole he's a decent enough fellow, he knows Chinese so he can communicate with our family, although he can also be a bit of an idiot at times, especially in social situations. My youngest sister's marrying a software engineer, he takes good care of her (she has a few health issues) in his humble, loyal, bumbling way. They're both all right.
For the second issue, we simply learned to accept it. Daughters get married and move away all the time in our culture. So they're only going to visit every few years, that's not too bad. We have the Internet now, we can keep in touch with email and Facebook and Skype. We can still be there for important events, such as the birth of children or major illnesses.
For the third and fourth issue, we learned to say "fuck it." Cultural gaps can be overcome as long as everyone stays respectful. We might not always be interested in learning or integrating into a foreign culture, but at least we can be respectful and not act like dicks. As for the societal stigma as a whole, fuck them. They don't know us, they don't know my sisters, they don't know their husbands. If people on the street want to give them dirty looks for holding hands with Caucasian men, then that reflects badly on the idiots on the street, not on my sisters.
All of this took time. That's what I think I should emphasize most. The elder sister was with her boyfriend for over ten years before they decided to get married, while my youngest sister was with her boyfriend for about five years. It takes time for people to get over their prejudices. It also requires a willingness to overcome the said prejudices, which again can take time to develop. It takes time to see these men as people, instead of anonymous barbarians here to abscond with our daughters. It takes time to appreciate the challenges, and to formulate strategies to defeat them.
Don't think this will be a quick or easy process. And don't try to push your parents before they're ready. That'll just cause the opposite effect, they'll hunker down and dislike your boyfriend even more. Have your boyfriend be the best possible boyfriend he can be, because believe me your parents will find any excuse to nitpick any issue they can find. ("Oh he drinks beer? You don't want to marry a drunkard! Oh he's a bit overweight? He can't even look after his own health, how can he look after you? Oh his job pays less than seven figures? You can do better than that! Oh he's trying to convince you to switch careers? He's such a bad influence!")
I wish I could tell you that there's a sure-fire route to success, but there isn't. I've seen other girls, some in my own family, who have tried to get their families to accept "unacceptable" husbands, and were forced to break up, or were outright disowned. Sometimes some people just don't want to let go of their preconceptions. Sometimes people just don't want to change.
Good luck, and please feel free to PM me if there's anything else you want to talk about.