I disable my old credit and debit cards with a hole punch. It removes the chip beautifully. The point being that your bank PIN is stored on the card itself (so much for the 'security' of chip and PIN).
Burning will deal with magnetic strips. Microwave ovens will also kill chips, especially RFID chips. At a guess you might also induce static, for example with a piezo spark generator (gas hob lighters, etc.), but you need to be sure to get the spark to land on the chip somewhere.
I note in passing that there is a circular mounting under the rim of Bristol council's new, downsized dustbin (right-hand end of the side opposite the hinge) for the RFID chip. I believe the idea is to have cameras on the back of dustcarts, pointing at where the bin's contents are tipped into (linked to RFID readers, obviously). Thus your rubbish will be on-record in case you dare to throw away anything that can be recycled.
Big brother is nothing if not resourceful (with other people's money, that is). The US' Mises Institute (economic think-tank) claim that curbside-sorted recycling (what Bristol now does) is nine times more expensive than using well-managed landfill. The point being, if there's no economic market for what's being recovered, it's far better to store it in landfill until it can be 'mined' later at an "eco-nomic" price.
Our waste paper is presently being trucked to Kent for 'recycling' - gotta be greener than a waste-to-power plant in the area (I don't think).
E. (the genuine environmentalist)