In his essay "What I Believe," E. M. Forster wrote the following:
If I had to choose between betraying my country and betraying my friend, I hope I should have the guts to betray my country.
This is the choice that faces Kate and Jim in All My Sons, though in Kate's case, her loyalty is to her husband, a bond even stronger than friendship. The issue is further complicated in Kate's case because she is living in denial and has forced herself to disbelieve in her husband's guilt.
The conflict between private and public duty is notoriously difficult to negotiate, but Kate does eventually find a middle ground which many audiences and readers will regard as reasonable. She does not report Joe to the authorities for his crime, but she does eventually confront him with it and demand that he should face the consequences. However, she does this for private, family reasons, because she wants him to placate their son, Chris.
Chris is the only one among Joe's family and friends who contemplates telling the authorities about his crime, and even he is conflicted about this. Kate, Jim, and Joe himself display no concern with public duty or with the moral consequences of the deaths Joe has caused. Joe's guilt is clear, but whether you think Kate and Jim participate in that guilt will depend on your stance on the question of whether private loyalty is more important than public duty.