As far as I'm aware, that illegality does not extend to purposes like costume play, drama, re-enactments, etc. Especially if it's out-dated military symbols from another country from decades in the past.
And your comment about Germans being sensitive about this comes back to the idea of context. Obviously, it would be in extremely poor taste to wear a costume such as this to a German convention, in Germany - again, for obvious reasons. But frankly, I don't see how any reasonable person could be offended by the costume of a fictional organization because it bears a resemblance to a real-world organization, not if it's done in the spirit of creativity and fandom, and in a place where one, as a rule, expects costumes of fictional individuals and organizations, outside of an area or other context that was directly, negatively, and hugely affected by the real-world organization. I think all of those things add up to make it perfectly acceptable to wear it in a convention in North America. In Europe? Not so much. On the bus TO the convention? Also not so much.
Also notice that I haven't said I'd be the one wearing this costume. Much as I like the hat, I don't think I'd want to wear it, for a lot of the reasons of taste that people have laid out here. But that's a personal choice - I'd say it's a perfectly valid costume for someone else to wear, again, given the proper context.
Whether people are too easily offended today is a whole other argument (for the record, I think a lot are, but dismissing them as such comes with the real danger of dismissing legitimately offensive things along with it), but it's an interesting point about laws concerning hate symbols. Obviously they can't be banned outright - not only would that make history class really confusing, but it would kill historical re-enactments and various theatre plays - and make a surprising number of films, video games, and television shows automatic blacklist candidates.
Once again I need to come back to intentions. I think as long as you're aware of the proper context and aren't trying to promote or say anything with it, you reach a point at which no reasonable person should be offended. Of course, I have to restate, I think there ARE certain symbols and costumes that would transcend that limit, the swastika among them - at this point it's just plain offensive, period, which is a shame, given that it was appropriated by the Nazi's and had an entirely different meaning beforehand.