Where does the additional mass come from when the fungi reproduces in space?
The most important measure for any radiation shielding in space is weight. We have great technology for blocking all radiation today: lead plating. This is obviously way to heavy for space. Alternative suggestions have been to surround the astronauts with water which presents a lot of challenge in terms of plumbing and weight. Having the walls covered in fungi may actually be a much lighter option, I certainly hope the idea is well considered.
Fungi aren't plants, though.
edit: they're heterotrophs - they get their food from more complex materials than autotrophs, which generate their raw material largely from carbon extracted from the atmosphere.
Except not these ones! These are autotrophs fungi, they do some kind of photosynthesis (it's absolutely not the same metabolic path, though) gaining their energy from gamma rays instead of food.
Edit: The above comment is wrong, I though autotroph vs heterotroph was about energy input (as a matter of fact I'm very convinced it was how my college teacher explained it) but from wikipedia it looks like I'm wrong, and such fungi would be classified as Photoheterotroph[1]
At least you can be using the water though.
There's plenty of radiation that we have no effective way of blocking, like neutrino radiation.
But that's about the extent of my knowledge.
Do you happen to know if in a composite shielding situation (several layers of multiple materials) would you put the lead on the outside facing the hard radiation, or on the inside?
If the shield is actually alive (say, a layer around your emergency shelter), then you can just fill the hole with food and let the fungi patch themselves, and any damage caused by being exposed to partial vaccuum. Possibly with a mold that also acts as a temporary, reusable patch over the worst hit areas, so that a subsequent space storm doesn't catch you with your pants down.
Growing shielding could be very good. Especially if you can use waste products to do so. The right sort will be easier to find on the right asteroid, but could be available on the moon if you have a high enough volume of imported supplies being turned into effluent streams.