Not only Asian women to be fair, but non-white women in general, although their reaction is more visceral in the case of Asian women.
The usual white women's reactions are:
#1 They say the guy can't get white women (as if Asian women were easier than white women, something we can all agree it's not the case).
#2 Show passive-aggressiveness and accuse both of having a race fetish, especially the guy ("He has yellow fever!").
#3 Accuse Asian women of being "colonized," "self-hating" or even gold-diggers. And the guy of exploiting them because they're "submissive."
Some even say insulting things about them and I've seen a few white women who were used to refer to Asian women as "whorientals."