Seeing that it is optional to report your ethnicity, I'm kind of surprised that anyone (other than those who get an advantage) would do so. The admissions system is already arbitrary as hell.
Why not just hide it from them? I suppose there are certain parts of an application which could give away information that’s meant to be hidden—being president of the Asian-American Student Club would pretty well give away the applicant’s ethnicity.
And then there's the whole "legacy admit" thing.