You do have a point. In case of credit card, when you volunteer your information ( and your permission to check information about you ) for the convenience of plastic, you technically do give up your data. But as a counter argument I would like to point out that that trade is restricted by various laws and compliance can be onerous. Now, I still did not see credible news of credit card companies selling personally identifiable data of, say, dunkin donuts users. But then, we all know of the story about store sending baby stuff to a family before parents knew their kid told them she is pregnant.
I don't use rewards programs ( though now those seem to have migrated to collecting phone numbers ).
But no, to answer your question, I don't trust them not to abuse this information so there are things I simply pay cash for. I think last time that issue came up for me was when one bank seemingly decided ( and backtracked ) that legal gun purchases are verbotten ( https://dailycaller.com/2013/01/16/bank-of-america-credit-de... ). Though that particular cases again seemed to deal more with individual specialist decision and was not a policy decision.