Is this information mandatory? i'm choosing to not identify my race and i don't want this to give it away. No, I am not asian (not that this should influence the answer to this question).
I don't think you will be able to submit the app without filling out all the required fields, with parents' information being one of them. You can, however, try making a point by purposely putting in "not comfortable stating" or "N/A", but with that you're also drawing attention to the issue to the admission office.
