When they get a "Confirmed" result, that's real data. The proposed effect happened under those conditions. When they make a number of attempts, fail, and label a myth "Busted", is when they're the least scientific. Later episodes may prove them wrong. Kind of ironic for a show named Mythbusters.
Anyway, back to the topic. Yes, your 21" CRT does indeed produce large magnetic fields when it is first turned on. There's a degaussing coil wrapped around the front of the tube, inside the enclosure. It's there to erase any stray magnetic fields on the shadow mask. It only runs for a short time.
Thereafter, magnetic fields mess up the picture, as anyone who has held a bar magnet up to a color TV or monitor can confirm.
If we could manage all those years sitting in front of huge degaussing coils, I suspect that our mag-stripe cards are pretty safe. Just exercise a little care.