Under the Constitution the only thing the government has a right to do under a census is get enumeration, or in simpler words a headcount. Anything beyond this is not in the Constitution. I will note that I am not a lawyer, but it is quite clear that government officials and law enforcement should not have the right to ask you for further information unless they have reason to believe you have committed a crime. In which case you should also have the right to remain silent under your 5th amendment rights as a US Citizen.
Call me suspicious of government when it comes to them asking how much you make, where you get it, how much you pay for insurance, what your race is and doing it all with a GPS device in hand to note your location, but I can see no good that could come from providing such information to them. On the issue of race I am joining others in checking the box "Other" and entering "American" as my write in and I urge you to join me.
According to the laws in this land race is not supposed to be considered in any manner. There are supposed to be equal rights for all and the noting of peoples race can only be used for harm. If it is used to increase funding to some sort of minority or majority cause then that is discriminatory against all others. There is no need for the government to request, nor use this information in any way.
All of the information they are asking for is no doubt going to be used in some sort of way - and as with all government programs will be to waste tons more money on ridiculousness or for nefarious reasons - most of those being to infringe on your rights further somehow.
Jerry Day points out some things to watch out for when the census comes to your door.