Perhaps if you just carry enough RFID credit cards jammed together in your wallet they might confuse the scanner enough to give incorrect numbers?. I think I know people who seem to be applying the theory.
A complete wrapping in conductive foil likely would work, or a metal box (something like some people use to carry their business cards) probably would provide adequate shielding for most situations.
Carrying the cards in a pocket where the scanner would have to be shoved in your face to get close enough might offer some likelihood that a scan would be more obvious, but the practicality of that would depend on clothing styles etc.
Tucking the cards in a "private area" would require a thief to "get personal" and might work for some people - but perhaps less well for some personality types.
In the video, it appears that the scanner must be within four or five inches of the card for a scan, but that may just be the kluge the demonstrator put together. Some "secure facilities" have been using RFID badges for more than ten years that are expected to be detected at "walking speed" so that the badge is read from a few feet away even if it's in your pocket, and the gate is supposed to open before you smash your face on it - but they don't always work if you walk a little too briskly. The scanners for such "long range" detection would likely be difficult to replicate in an inconspicuous portable package.