Before digging into this question I want to address the ways in which Liesel challenges her society. In some ways she is not very different from the kids around her. Like any child, she likes playing games and doesn't much like school. However, as the book progresses, she begins to change and to see things differently.
One of the ways that Liesel challenges society is by stealing books. She steals first The Gravedigger's Handbook and then continues to steal books throughout the story, including books which were meant to be burned. She doesn't understand why society bans certain books, instead wanting to read everything she can get her hands on.
The introduction of Max is a new way for Liesel to defy society. She herself doesn't have much control over the situation. Although she was not the one to invite him into the house and agree to hide him, she begins to befriend this character and finds herself again at odds with society.
There are many ways in which these small acts of defiance affect those around her. Rosa tries to tell her to conform, while Hans in some ways follows her in going against society.
We see a positive effect when Liesel reads to her neighbors while they wait in a cellar during a bomb raid. Her love of stories, though once forbidden, becomes a way to calm everyone and get them through the tension.
We also see the negative effect of going against society, not so much through Liesel as through Hans, who puts himself in danger by offering bread to a starving Jew. There are consequences for trying to be different from society, and The Book Thief shows us those consequences at the same time as it praises Liesel's ability to see things differently.