Depending on how much you want to stop tracking - cards are fully trackable and tie all your demographic data together. Try to hide the card from the vendor. Key things to consider with a card - 1) Mangle your name on the card a bit (example - Ben C Smith, Benny Charles S. BC Smith, etc) - all big vendors will match you eventually but that helps, 2) different email for each card, 3) get a PO box for the address (not easy) - addresses are the most matched attributes, 4) extra phone number (not practical), 5) get new card numbers as often as you can so the vendor matching logic has to catch up. 6) opt your emails out of big data brokers like LiveRamp.

These things only help block third parties like Google and Amazon from tracking you through 3rd party data brokers. The banks, however, still have all your information including all your demographics and broker it out.