It is physically impossible for X-radiation to affect magnetic recordings. Data density on computer disks is far higher than that on audio tapes, and changing a single bit of computer data can thoroughly screw things up as opposed to (perhaps) a barely noticeable blip in an analog audio recording. Yet tens of thousands of computers go through X-ray screening every day.

The cautions in the Sony Web page are not about X-rays. They are about (a) a different kind of screening and (b) the extremely remote possibility of stray electromagnetic radiation from the conveyor belt's drive motor. Following them (except #3, see next paragraph) can't hurt, but be aware that it's almost certainly not necessary.

(I don't see what good it will do to carry a sample tape they can X-ray, though. Can you imagine TSA reaction to hearing "Please don't X-ray that one, you can X-ray this one, they're the same, trust me?" Sounds like a request for secondary screening to me!)