What did Miss Maudie mean when she said " Atticus Finch is the same in his house as he is on the public streets "
Atticus Finch is a character who lives by his own principles. He is steady in his beliefs and doesn't compromise his ethics because society may think something different. He doesn't put on a front. He treats everyone the same, and therefore would be the same at home as he is in public. He doesn't feel like he has to be anything that he is not. It is this steadiness that people of Maycomb rely on. That is why he is asked to defend Tom Robinson, and why he comes to Boo's defense with the sheriff at the end of the book. His teachings to Scout and Jem are life long lessons. He will teach them about respect and finding goodness in everyone. He will teach them patience and to look at the world from other peoples' perspectives. He treats everyone the same no matter who they are.
Often we feel like we have to play out a role or "wear a mask" to fit into society. We sometimes go against our basic beliefs and values to fit in. You won't find Atticus doing this as he is stalwart in his convictions.