I think there is a difference between race and culture. Usually these two things go together and hence can lead to problems in a long-term relationship when cultural traditions and values become relevant. Its the reason why Jews strongly suggest marrying other Jews so that the tradition can be firmly passed on, some people consider this a race issue but it is not, its a culture issue. Simply it is easier to raise a family and live together in a specific group if race, culture and to a lesser degree background are similar. You say you are Asian then you probably know that Koreans and the Japanese frown on inter-racial marriages no matter what the other race and the children are usually ostracized. In the case of the Japanese they are put off by anything that isn't Japanese, so it would not matter if the partner was Chinese or Thai, they would frown on the union. Personally I would not enter into a relationship with someone who had a drastically different culture than my own, so for example if I dated an Asian he would have to be sufficiently westernized. Culture matters more than race but the two can go together so if I came across someone who's family were offended by my race then I wouldn't even bother taking the relationship seriously because in the long run it would cause too many inter-familial problems, too difficult and not worth it.
Norsefire: I don't think it is racist to want to date within ones race exclusively. Racism is prejudice+power, not preferences on who one wants to eat, sleep and create a family with or who one finds attractive. I find very few Asian men attractive but I this doesn't make me a racist but its not because I have some bogus notion of racial superiority. If you have a scale of which race is 'worth' more then something is skewed in your thinking. To prefer your own race to others is a matter of preference but it doesn't make your specific race any more 'worthy'.