In The Boy in the Striped Pajamas, throughout most of the story, Bruno has little true understanding of what the Nazi youth does. In his naïveté, he watches and believes the propaganda films portraying the unrealistically pleasant life in concentration camps, and so his view of the Nazi Youth is certainly skewed.
It seems he is more irritated throughout the story about his older sister's pompous nature and the sense of superiority she takes from being a part of the youth movement. Her condescending attitude grates at him and drives him farther away from those activities as he becomes closer to the boy in the striped pajamas. Based on his kind nature, if he was aware of the atrocities committed by the Nazi Party and, in turn, the Hitler Youth, he would have been mortified by his sister's involvement. As it were, however, he seems rather dispassionate about it.
Bruno and Gretel have limited interactions; as brother and sister, they are not very close. She is the more informed older sister and often comes off as a bossy know-it-all. As such, Bruno's judgment in terms of her involvement in the Hitler Youth, and anything she does in general, is likely clouded. In comparison, Bruno reveres his father, a commandant in Hitler's army. He brags to Shmuel that his father is a good soldier because he was promoted to a high rank and wears an impressive uniform. Bruno, being a nine-year-old, knows very little about the Nazi party and the Hitler Youth. He is more fixated on the fact that his father is a good soldier than he is on the fact that his father is contributing to the Nazi cause (an undeniably horrific cause, but in their perspective, a cause nonetheless). Based on the little information provided in the text, in terms of Bruno's references to his sister and his internal reflections, I would argue that he is indifferent to the fact that she is part of the Hitler Youth.