Yes, we are supposed to fill out our census form accurately. There’s a penalty for not doing so.
Obama represented himself as being only of one race (the least significant contribution to his genome and upbringing) on his census form.
It is most appropriate for people of mixed or uncertain ancestry to leave the race portion of these forms blank.
Number one, it brings forth the idea that race is not such a big deal since most people are acturally mixed race if one looks back far enough.
Secondly leaving a blank spot or checking ‘other’, when possible, averts the problem of inaccuracy.