While I myself have no problem with interracial dating, living in Malaysia, I can see why some people would be uncomfortable with it.
It seems to me that for the most part, people are unsupportive of interracial dating due to differing cultures. Here in Malaysia, the 3 largest races are Malay, Chinese, and Indian. The cultures and traditions of these races tend to clash with each other, and if our parents are very traditional, you can bet they'd discourage you from going out with someone of a different race.
Especially when it comes to Malays. By Malaysian law, all Malays must be Muslim, and any non-Muslim who wants to marry a Muslim must be converted to a Muslim first. With the numerous Muslim traditions viewed by many others as tedious (including praying 5 times a day, fasting for an entire month every year, women being required to wear head scarves and so on), interracial marriage becomes scarce. The older generation tells us how we shouldn't marry people from other races/cultures because they conflict with our own.
I guess what I'm trying to say is that when it comes to interracial dating/marriage, culture can be a pretty big factor when race isn't.