the census: an enumeration, not an interrogation
The Constitution provides that every ten years, the Federal government shall conduct an "Enumeration" of the people, for the purpose of apportioning Congressional representation.
It does not provide for interrogating the people about race, ethnicity, family relationships, home ownership status, or any other information. (I got the "long form" back in 2000, which had over 50 questions; they seem to have done away with that one this time, though.)
Before you provide such information, feeling assured that it's private and protected by law, you might want to consider that the Census Bureau provided the U.S. Secret Service with names and addresses of Japanese-Americans during World War II so that they could be herded up and put in concentration camps.
It's not that I'm expecting any such round-up to be repeated any time soon, mind you; it's a matter of principle. The only thing the Federal government needs to know for the census is how many people live here, and that's all it's going to get from me. If it wants more information, it can get it with anonymized surveys.