I understand wanting to keep the police out of your private things. But we already let them in when they have a warrant. Are you saying DNA is more private than your house, computer, phone converations, etc? Or that all those things should be off limits to police with a warrant?
Of course this is not the same as giving them free access to whatever they want. Then I could understand people's worries. Individual policemen could use it to harass people they don't like, or other abuses.