This is one of the few situations where my English is not good enough for a long exposition of my thoughts. But there's no real need to do that since Joe Offer in his last post has beautifully said what I think. I'm against censorship except in very very few situations and this is one. This song should not be played at least in Germany at least as long as any survivor of the concentration camps is alive. The song, even the tune alone, will bring up memories for them of a brutality beyond expression. Some of them relive torture when they hear this song again. We should be decent enough to spare them that.
It's not the actual words in that song that make it a no-play song, it's its association with that terror time. The song is not just any Nazi hymn it is the Nazi hymn for it was played regularly just before the National Anthem.

Wolfgang

some additions: Yes, the tune was taken from older sources. Look up Der Abenteurer for an older German song using that tune. Of course, the Horst Wessel Lied has had its parodies during the Nazi time, like singing "Die Preise hoch, die Schnauze fest geschlossen" (up with the prices, shut up your mouth) instead of "Die Fahne hoch, die Reihen fest geschlossen" ( look here for a full German version of that parody following closely the structure and lyrics of the original). The difference between singing or (in German English:) sinking these alternative lyrics could be the difference between being dead or alive then.