I would be hesitant to reduce Anne Frank’s diary to one moral or to even a few morals. Anne Frank is one of the most iconic individuals in Western history and perhaps in the world. Yet remember, before Anne became an icon, she was a person. She had flaws and prejudices like any other person.
Perhaps I've inadvertently stumbled on a moral you could talk about. You could discuss how honest and truthful Anne is. Even when it makes her look bad or unfavorable, Anne writes it down. Anne doesn't seem to feel the need to repress or censure her feelings. She’s completely—sometimes cruelly—honest.
There's many examples of Anne's loyalty to her true feelings. Some are negative and some are positive. The ones that are more negative tend to link to her mom. As you might already be aware, Anne had a contentious relationship with her mom. “I only look at her as a mother,” writes Anne, “and she just doesn’t succeed in being that to me.” Anne is harsh. Yet sometimes honesty is harsh.
Of course, not all of Anne’s honesty relates to harshness. She’s also sincere and forthright about her developing sexuality and her attraction towards girls. Anne’s candidness has to lead to censorship. Her father removed some outspoken passages before it was first published in 1947. More recently, in 2013, a parent tried to get the book banned due to its explicit passages.
Besides unconditional honesty, another moral or virtue that comes to mind is "be yourself." It might sound cliche or trite, but Anne’s diary is a testament to the power of remaining true to who you are. It doesn’t seem like Anne tries to simplify or confine herself to one kind of person. Throughout her diary, Anne is sad, happy, amorous, manipulative, sweet, vindictive, selfish, generous, and more. Basically, Anne is a dynamic person. Her loyalty to her complicated, messy, ever-changing identity seems like a central virtue—or moral—to me.