I think it's the same point - you could indeed track people by DNA if there were a general DNA database, but a lot of people object to that in the same way as they object to finger-printing. Generally only convicted criminals lose control of either of those markers, the only common exception is where people have committed no offence beyond travelling to another state. Many Western states have a long way to go to demonstrate that their systematic surveillance of citizens is proportionate and adequately controlled by law.
I take your point, that objecting to this sort of surveillance is really pi$$ing in the wind of technological reality, but some people may choose not to make it any easier for Big Brother (be that the State, Google, Visa , TelCos or all together) than is really necessary.