Privacy violations are NOT a necessary evil. They are the slipperiest of slopes. Look to china to see where this road ends. The government is not our parents, it’s a naughty power hungry child.
The tendency now it seems is for people to absolve themselves from maintaining a democratic discourse by taking a selfish absolutist position.
There will always exceptions.
The main problem is that most governments have historically shown themselves to use every possible angle they can come up with when they want to go after someone, no matter the legal stretch. Thus, collecting data that could be vital to a legitimate concern could also be later misused for other nefarious purposes. If governments would be the "bigger person" so to speak, and not stoop to dastardly levels, more people would have faith that the government would not infringe on their inherent rights without a damn good reason.
The reality is that vaccination has been a requirement to participate in society for decades. You have to be vaccinated to go to college, your children must be vaccinated to go to school. And if you want to travel countries will demand you provide proof of vaccination so that you're not a walking bag of diseases.