What does Jewish discrimination, Hitler's propaganda and the Hitler Youth have in common in The Book Thief?

In short, the answer to your question is that the reader is able to observe discrimination against the Jews and the propaganda of Hitler through Liesel joining the group called Hitler Youth.  In other words, two of the major issues of the Nazi Regime are revealed through its group for the young people of Germany.  It is within Hitler Youth that young Germans are taught to discriminate against Jews and forced to accept Hitler’s propaganda.

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In short, the answer to your question is that the reader is able to observe discrimination against the Jews and the propaganda of Hitler through Liesel joining the group called Hitler Youth.  In other words, two of the major issues of the Nazi Regime are revealed through its group for the young people of Germany.  It is within Hitler Youth that young Germans are taught to discriminate against Jews and forced to accept Hitler’s propaganda.

Liesel learns quickly that Hitler Youth is not just a “brown uniform,” but a method of brainwashing the young.  There are many examples of Hitler’s propaganda within the Hitler Youth, but one of them is stated here:

[Hitler Youth] would commemorate not only the Fuhrer’s birthday, but the victory over his enemies and over the restraints that had held Germany back since the end of World War I.

In other words, it is true propaganda to claim “victory over his enemies.”  There are no literal “victories” over “enemies” here.  Further, the “restraints” are then literally “burnt” as the Nazis burn books in large bonfires.  Any newspapers or books that are in contrast to Hitler’s plans are destroyed.  The young people are then taught to discriminate against Jewish people by supporting the forced emblem of the yellow star.  Hitler Youth are also taught that the Jewish people have had a negative effect on history (and especially the history of Germany).  Further, joining the Hitler Youth was more mandatory than voluntary.  Anyone who did not join looked like they were against Hitler which was not allowed in Nazi Germany. 

People like Liesel were constantly “skipping Hitler Youth meetings” and simply trying to “survive” being a member of a group which demanded such belief in both discrimination and propaganda.