How much weight does race carry in my application, and should I even report it?

On the Common App, race is not required, but I know that race affects admissions. I’m Asian (Chinese) and White (German) (both my parents are natural born citizens and got their educations in the US), and I’ve heard that Asian-Americans are considered the “New Jews” by some since some schools have (or seem to have in the eyes of many) quotas on how many Asian-Americans they accept. On my app should I include my race at all? I feel like not including my race would only hurt my chances despite it being an optional category, since there’s lots of emphasis on diversity.