Layman question: Is it possible to shield electronics against cosmic rays? Or is it like a neutrino thing, where they just go through everything? (But neutrinos barely interact, correct?)
That's not what actually happened here (probably), but think of relatively heavy atoms like iron, ejected from a supernova at close to the speed of light. They're not really "rays". They're solid particles that punch holes in everything. The good news is, mostly they're ionized and they get repelled away from hitting the planet's surface by our magnetic field (generated by the big hot iron magnet that's churning under our crust). But in the rest of space where there's no field like that, getting lots of tiny puncture wounds from high-velocity iron particles is pretty normal. It does a lot of damage to cells and DNA in a cumulative way pretty quickly.
To answer your question, shielding is possible but it is much harder in space than it is under the magnetosphere. Even so, a stray particle can wreak havoc. Shielding for the purposes of data protection on earth is essentially a risk/reward analysis. Anyone could get hit by a cosmic bullet, but the chances are pretty low. The odds of an SSD flipping bits on its own are significantly higher.