You said that it's okay for the minority of people to intermix, so I want to know why you think it's okay. Obviously there is going to be some, agreed - however this doesn't make it "okay" in your view does it? And what if the minority become the majority of people who intermix - would that not be acceptable to you? Why?
The reason why an Asian woman and her family wouldn't be okay with it is due to family traditions and cultures - in saying that, that is the view of a previous generation. And in future generations, I feel this will become less and less of an issue as immigration and ethnic diversity will happen - it's inevitable.
The reason why I personally feel it's "wrong" for you to think that is because there is no reason for you to feel that way. Why is it "best" for your race. What are you "protecting" your race from? If we do choose to intermix, what are you afraid will happen, or result in? I'm trying to comprehend the exact reason you feel the way you feel.
https://www.psychologytoday.com/articles/200601/mixed-race-pretty-face ---> check this article out, there's actually a number of benefits, only a few mentioned here, which mean that it's potentially advantageous to have a genetic mix of some sort. If anything, it's a preference to be mixed ethnically, physically, visually, and medically.