If the people vote for the government to collect everyone’s DNA at some future point in time, that’s just how a democracy works. Freedom and liberty includes the freedom and liberty to make poor decisions.
The majority vote can be rallied through fear and propaganda into vesting ever greater authority in a centralized seat of power, with any opposition vilified as an existential threat.
The only way democracy survives is through a watchful and untrusting populace that constantly holds its government to account and seeks to limit its power and pervasive reach into the lives of the citizenry.
Freedom and liberty require at its core the ability to dissent. Dissent in turn requires privacy because dissent by its very nature will be suppressed by those in power.
I would theorize that mandatory en masse DNA cataloging is anathema to democracy because it inevitably is far too powerful a tool to suppress dissent.