“Since ionizing radiation is prevalent in outer space, astronauts might be able to rely on fungi as an inexhaustible food source on long missions or for colonizing other planets,”
It's an interesting thought that our future Buzz Aldrins and Neil Armstrongs may be sustained by a diet of radioactive mushrooms. That sounds like a Marvel origin story.
One important detail is that the funguses are not necessarily radioactive [x]. They absorb the gamma radiation, that it's similar to the X-rays. After a radiography, x-ray or gamma-ray exposure the things don't become radioactive. But too much radiation kills almost anything. This process is used to produce irradiated food (http://en.wikipedia.org/wiki/Food_irradiation) that is safe for eating (when the irradiation is done properly).
[x] The funguses inside Chernovil are surely radioactive because they also absorb the water that is contaminated with radioactive elements. Don't eat them :).
http://en.wikipedia.org/wiki/Radiotrophic_fungus