Presumably, you are of the mind that the government also has no interest in gathering information on the spread of communicable diseases, HIV, cancer et al.
If so, then you are consistent, wrong but consistent. If not, then your opinion is relatively useless.
No they don't have the right to dig into people's records to find out if they have AIDS either, AIDS, whether I use birth control, ephedra, require racial information gathering... all of these ways government inserts itself in the name of 'justice'.