Disposable gift cards can be loaded with up to $500, and cost about $5.
If you buy your cards in cash, they're about as private as the security cameras are in whichever convenience store you pay for them in.
Based on what we know about Target's shopper surveillance and behavioral identification efforts being capable of targeting pregnant women with pregnancy products, who didn't even know they were pregnant yet, themselves, even seemingly benign store locations can be pretty lacking in actual privacy.
Between electronic survellance of mobile device identifiers, blue tooth signatures, free wi-fi usage, versus brute force video analysis yeilding facial recognition results for targeted ads on flatscreen monitors as you pass by bus stops, the status of tracking in public spaces is weird, although you really can ditch credit card tracking.
The only problem is, the truly huge companies have assuredly been routing around that idea for years, by diversifying their information channels.