To add another dimension to your question, I've read questions that ask why black men are okay to dating outside their race, but black women are not. Instead, they apparently just yell at "their" men and call them traitors for not sticking to their own race. I've given them another perspective, like maybe we do want to but we are afraid that the other races will reject us, especially since we've heard stuff about how bitchy and trashy and rude we are from other races. (Really? You won't date me because of those "video ho's" on music videos? Thanks much...)
But back to your original question...I think those who don't date outside of their race, or those who won't date black people, are trying to "preserve their culture" as best as they can. Getting with a white person doesn't necessarily do that, but hey, at least it's better than marrying some "ghetto" girl from the street. Truth is, the media portrays us as...well, you see. And then there are some idiots who prove the stereotypes by not daring to exhibit intelligence. So the Asians who don't date blacks are appalled.
This is just my theory here...because I am not Asian. And even though I have plenty of Asian friends, I've never bothered to ask them about their strict cultures. They usually explain it away with "It's an Asian thing," which I guess means they just don't want to go into it because it's so different that they're afraid I'd ridicule them or something. Anyway, it would be interesting to hear what an actual Asian guy thinks.
Don't be afraid, and look for the Asian men who like black women...believe me, it definitely does happen. In fact, anything goes nowadays.