The cost of the “free” stuff is covered by the profits they make on other products. It’s also offset by the data they’re selling about you.

The former is a classic prisoner’s dilemma, and with the way things are, taking part in the scheme is probably the better choice. If you don’t take part, you’re funding the people who do, at no benefit to you, unless enough people choose to opt out of the program to make it infeasible.

The latter poses a difficult problem. You can sort of work around this issue by taking multiple cards, providing a fake name for good measure (they’ll be more interested in your general area than your name in the first place), and most importantly, sharing and exchanging cards with friends and family to hide your personal data. Through some rather basic clustering analysis, these companies can still figure out your individual spending patterns if you’re sharing the card with a select few people (i.e. your household/roommates), but that’s an extra step they’d need to take that would probably only make sense if enough people would do it.

As (seemingly) nobody bothers with this privacy stuff, you’d probably be able to keep a bit of privacy by exchanging random cards with a small group of people.