That's a very slippery slope line of thinking, and having tendencies to date one race and reject another doesn't make one a racist. And I say this as an Asian man who has been hit by all the "unmasculine" stereotypes of Asian males in the real world, and studies have shown that Asian men have the most trouble in online dating. But I never once said or seriously thought "Women ignoring me on dating websites are racist". That's just not true, I'm never going to make that accusation despite my own struggles, and that's just a dangerous line of thinking that I just block from my mind, despite the temptation for my brain to go there in my darkest moments.
I get what you're saying, I'm not talking about individual attitudes here, but the aggregate across the entire country. In general, Asian Americans do intermarry at pretty high rates. For example, from the Pew study from 2017:
While 24% of foreign-born Asian newlyweds have a spouse of a different race or ethnicity, this share rises to 46% among the U.S. born.
It is of course a bit skewed by gender as well, but the fact remains that among U.S.-born Asians, about half outmarry. Which means - if there wasn't a constant influx of new Asians coming from overseas - the amount of part-Asian people would continue to rise, and the number of pure Asians would shrink.
Same thing happened in the U.S. with Jews. There used to be a lot more anti-Semitism in the U.S. a century ago, but now it's lessened, and around half of non-Orthodox Jews marry outside of their faith (60%+ of those since 2010). It's resulting in a lot more people of partially-Jewish ancestry as time goes on. And as a result, the number of Jewish people who aren't Orthodox is dropping over time.