Whether or not you want to apply the term "radioactive" to a black body emitter is completely beside the point, which is that EM radiation doesn't make things radioactive. Your objection is to the use of a word, not the physics, so I think this discussion has run its course.

At high enough photon energy, electromagnetic radiation actually can make things radioactive. The general term is "photonuclear reactions."

Here's an example:

"Photonuclear production of medical isotopes 62,64Cu using intense laser-plasma electron source"

https://aip.scitation.org/doi/10.1063/1.5100925