I did some research and the 2nd and 3rd verses are forbidden to be sung. Neither of them are Nazi-supporting but I guess the German Army has its reasons.
They glorify German militarism. Similarly, no one sings the first verse of
"Deutschland über alles", because of the association with the Third Reich, it's the third verse which is now the official anthem of the Federal Republic:
"Unity, justice and freedom/for the German fatherland
Let us all strive for it/brotherly, with heart and hand
Unity, justice and freedom
Depend on fortune
Blossom in the glow of that fortune
Blossom, German fatherland"
And you have to be a German major like me even to know that the song was an anthem in the old
Kaiserreich, though not the official anthem, which was
Heil, Dir im Siegerkranz (sung to the tune of "God Save the King"/"My Country, 'Tis of Thee").
As a song, set to a melody, it acutally consists of a piece written by Haydn (it is a movement from the "Kaiser Quartet" of 1797), with a poem written by Heinrich Hoffmann von Fallersleben in 1841, during the budding national movement that led to the revolutions of 1848. His poem was entitled
"Das Lied der Deutschen" ("the Germans' Song") and expressed the repressed hopes for a united national state.
Along with the first verse, which was meant to state that for nationalists striving for a united Germany, Germany must be above all other causes, there is a second verse, extolling the virtues of German wine, German women, German loyalty and German song (of course, the Romans would have had something to say about German loyalty, cf Teutoburger Wald and Arminius-even during the national movement in the 1840's, there were those who still argued for loyalty to the tribe-Bavarians, Swebians, etc, instead of a central nation-state).
In any case, strong nationalism and militancy was bred out of the Germans after the Second World War, and some of the trappings of patriotism or military spirit that we take for granted here in the US, or in other countries, have been suppressed in Germany since the war.
Prost!
Brad