Only criminals would object to a DNA database, wouldn't they?
Junkfood Science: Ingsoc
...While national security or science for the common good might sound like noble reasons for governments to gather genetic material of its citizens, that’s not what this is really about. And the potential for abuse and financial and political gain go far beyond anything George Orwell even envisioned.....As one of the public commentators at the Times insightfully noted: “They want your DNA because of all the information it reveals about you. As the human genome is decoded, government, employers, insurance salespersons, banks, and everybody else will be able to read what diseases you are genetically predisposed to and make decisions affecting you without your control. Government et. al. will have this increased power over you, but you will not have any more power over your government. In fact, it is just one more means of rendering you helpless and vulnerable to the whims of bureaucrats who have their own interests in mind, not yours. Eventually all people will be monitored and controlled from cradle to grave - the journey of which is adjustable by those with enough power.”
This is so much bigger than public health and safety.