I am not too sure that "immature" is the right word to describe Chris Keller. I would definitely want to describe him as an idealist and perhaps somewhat naive about the state of the world and man's role in it, but immature is perhaps an innaccurate description to apply to this central character.
He certainly does have an idealised picture of what he thinks life should be like. Note his conversation with his in Act One when he talks about his plans for the future and how the family business does not inspire him:
If I have to grub for money all day long at least at evening I want it beautiful. I want a family. I want some kids, I want to build something I can give myself to.
Whilst we can appreciate the high morals and expectations in his words, perhaps we can also reflect that he has a very idealised picture of what life is like and what he can expect from it.
Likewise, he has very strict and unyielding notions of justice and right and wrong, compounded by the guilt he feels at having survived the war when so many of his friends perished. Note the way his high ideals are expressed when he tries to convince Jim Bayliss to leave his profitable medical practice to pursue medical research, a supposedly "higher calling." Ultimately it is these higher notions of what is right and wrong that force Chris to see that his father must return to jail for what he has done when the truth of what happened in the factory emerges. Thus immature is not entirely accurate, but Chris Keller can definitely be described as naive and having a very strict notion of nebulous concepts such as right and wrong.