I've heard the opinion expressed multiple times that Asian Americans who are dating or married to white people should not be activists. I disagree with this opinion because it does not take multiple facets of activism into consideration.
There are many different ways that a person can help out Asian Americans, regardless of their race or the race of their spouse. If you are going to be a high-profile spokesperson, I would say yes, ideally your spouse should be Asian American, or you will alienate a lot of people.
However, if you are going to support Asian American artists/film, donate money to causes, teach a class about racism, protest a racist incident, pretty much anything where other people will not be turned off by your personal life because it's not a question, then it's fine.
We don't have the numbers or the support to "kick out" everyone who marries "out". As for their white spouses, white people can do a lot in dismantling racism by talking to other white people, who are more likely to listen to whites.