I think it was supposed to be inadequate shielding on the station itself that was the problem, as those on the ships seemed fine...
Yeah. That's what I think too.
In order to be able to live long term on a vessel in space, it's assumed that the colonists materials technology would have reached a level capable of solving the problem of shielding occupants from cosmic radiation and solar particle events (the only other practical way is some type of EM or plasma shield, which just isn't a part of BSG...like energy weapons). Any material that could protect against cosmic radiation and solar particle events long term, across the full EM spectrum, would easily protect against the radiation in the environment around the station (and additionally, easily shield against space detonations* of nukes).
If it was an EM field and not radiation, Galactica was specifically hardened against such things. It was an older battlestar that Adama had specifically left un-networked and EM shielded so the Cylons couldn't induce signals or viruses in it's systems - unlike the newer battlestars. Of course though, that hardening wouldn't necessarily protect biologics, it could only be a part of systems through shielding of wires and such. But it is possible that the skin/shielding material of Galactica may protect against this also, though it's never discussed. A material capable of shielding cosmic and solar particle radiation, would probably be very conductive - possibly even bordering on super-conductivity. Such a material would provide significant protection from an EM field by channeling lines of flux through it's own material, rather than the internal materials it surrounds (which is basically how EMP shielding works). This would be even more effective if internal materials/structures were isolated/insulated from the outside skin/shielding (though structurally, probably very difficult to do).
But this is probably all overthinking it quite a bit. For all of BSG's attempts at visual and conceptual realism, it's still just a fictional narrative - a narrative that in the end is going to put story and plot ahead of most everything. It's hard to believe that a station in such an environment wouldn't have proper shielding. Without such shielding it would be virtually unusable: long term occupation would be impossible from biological effects, electrical systems and components would eventually degrade to a point of inoperability, etc. But, it was necessary for the story - so Adama could learn of the existence of Human-looking Cylons. Thus the station is unshielded despite the illogic of it. Another such instance is when the Galactica is hit by a Cylon Nuke. The people inside the ship feel a shockwave (highly mitigated and surviveable, but a shockwave none the less), and there are electrical system failures and fires due to EMP. But since viewers don't know this wouldn't happen (and possibly the writers didn't know either), and since viewers think of Nukes as massive weapons (which they are - but they still follow the laws of physics), then viewers expect to see a big reaction to a Nuke hitting the ship. Because viewers see a big reaction, but overall minimal damage, they resultantly think:
"Nukes are tough...but Galactica's tougher - COOL!" - which is probably the exact response the writers wanted. (Hell, I
do know what's supposed to happen, and I thought that scene was seriously cool!

) In reality, nuclear weapons for ship-to-ship combat in such a future environment, would likely be impractical. As a result ship-to-ship Nukes probably would not be developed, or even explored. Planetary bombardment however is an entirely different story.
*Space detonations (outside of a planetary atmosphere and EM field) of nuclear weapons are essentially just big, radioactive particle generating flashbulbs. There's no pressure (shockwave), thermal, or EMP aspects to contend with. If in proximity to solid matter, the released particles can cause an ablation of suface matter, and there is some particle pressure, but if it's made of material already capable of long term shielding against cosmic radiation and solar particle events (without generating large amounts of secondary radiation), a nuke isn't going to be a very big deal. It might be a good idea to replace the shielding/skin material at the next opportunity, but short term it's not a problem.
Pressure (shockwave) - requires interaction with surrounding matter, whether atmosphere, liquid, or solid matter (like the inside of a comet or asteroid). If not surrounded by matter but interacting with a surface in a vacuum, it's particles only cause ablation of surface matter.
Thermal - the fissionable material will be pretty hot, but in space it will dissipate quite quickly, since there's no atmosphere to superheat into plasma. Any material capable of handling large scale solar particly events would hardly be effected.
EMP - EMP from atmosphic and low-orbit (high-altitude) detonations is due to two different things interacting with the planets magnetic field: gamma rays from the detonation itself (E1 pulse) and ionized particles from the atmosphere (secondary radiation - E2 pulse) - (there is a third pulse from a detonation - called E3 - that happens because of alterations or "pushing aside" of the Earths magnetic field due to both of the above sources).
Portrayal in the show/miniseries of a nuke causing a shockwave upon detonation with the Galactica, and EMP induced electrical problems and fires inside Galactica, are completely inaccurate. If enough particles were able to penetrate into the ship, or were generated as secondary radiation from the skin/shielding material, to cause EM problems in the Galactica's systems, evey person on board would immediately or eventually die from radiation poisoning...
In order for a Nuke to be effective against the type of skin/shield material necessary for interplanetary/interstellar travel, it would need to have some type of kinetic penetration capability - in which case a high-explosive or thermobaric detonation would be just as effective, and a lot more practical.