I did that ten years ago. Somehow, the Census Bureau got hold of my phone number and called my house to find out what race I was. I wouldn't tell them. The census worker explained that they had to know my race. I replied that it was a violation of the Civil Rights Act to take race into account for any actions I did, and that included filling out a census form. She finally gave up.
bump 38 and 39
I just answered and sent back my census. I did fill out ALL the questions, but I put down “American” as the answer to my race, as well as my wife and ALL my kids. We’re all Americans.
If they call me, I may just answer them the way you did.