Irradiation is not safe.
Irradiated food has been nuked with evil ionising radiation! The sky will apparently fall if we import some juicy tomatoes from tropical Queensland.
But there's some sense from the font of knowledge that is Wikipedia.
Food undergoing irradiation does not become any more radioactive than luggage passing through an airport X-ray scanner or teeth that have been X-rayed.
Some of the more fervid no doubt might posit there's a conspiracy afoot in the report Wikipedia references.
I'd suggest that the Chicken Little in residence over at FrogBlog needs to dispense tinfoil hats post haste. After all, the ionising radiation pouring from cosmic rays, x-rays, cellphones and the like must also be stopped. Whilst on the subject, I do wonder how much cumulative radiation has amassed in the green MP 'Ronald' Hughes from rushing around the country's airport scanners.