You'd be surprised how many paranoid people don't actually understand what it is they're being paranoid about. There are people who, for example, won't enter their credit card number into an electronic system because they're worried someone will steal the details, so instead speak it aloud over the phone in a room full of people.
Here in Australia there was also some kind of single card for some array of services or other (health, maybe?) that the government wanted to introduce, being sold to the public on the basis of it being a convenient way for them to co-ordinate all these services, rather than getting Form A from Department A to submit to Department B so they could get Form C to submit to Department C so they can get Form B so they can go and get what they actually want from Department D. People raised a huge fuss over privacy concerns, and how this card would be used to track people, and all that, and eventually it was scrapped. The people celebrated because they'd defended their privacy. But the various departments talk to each other behind the scenes anyway, and bit by bit legislation to allow the departments to do what they were going to with peoples data passed, leading to the end result where people are tracked anyway but don't have the convenience they could have had.
So the moral of the story is, if you're objecting to some offered convenience because privacy, either think about and object to all the other ways the involved parties could get your info anyway, or just take the convenience on the basis that you might as well have that if your info is going to be passed around anyway.