Unless the premise: "It is possible to understand truths about god" is accepted, then any statement about "god" is unintelligible. This includes the statement "I don't believe in god".

This does not seem to allow for personal perspectives. Regardless of if God exists and regardless of viability of comprehension, if one does not personally believe, then what more do they need to tell you? Even if they are making a more gnostic "strong atheist" claim that God definitely does not exist, it is still from their personal perspective and, regardless of whether they are right or wrong, you know what they are saying.

I was aiming for a logically defensible categorical distinction.

I suspect you will find that a difficult task. The only definitive categorical distinction was the first one I provided. The second one, concerning the manner in which they think, might be a pretty common distinction that is supported by studies, but is still a generalization, not to be taken as a universal categorical. Approaches to both theology and atheism are potentially wide-ranging, and there are people on both sides whose reasons for affiliation are not logical or sensible to outsiders, but make total sense for the person using that reason.

There's something of an atheist paradox though. Unless the premise: "It is possible to understand truths about god" is accepted, then any statement about "god" is unintelligible. This includes the statement "I don't believe in god".

Devil's Advocate (lawl): Wouldn't presenting the bible, whether in whole or in part, as the word of God be a case of understanding truths about God? I figure that atheists and theists alike accept the premise you've proposed. "I believe in god" is equally unintelligible without accepting that premise.

That is very unlikely scenario. How would the person justify something like that (to him/herself)?

Congratulations, you have discovered a great truth of humanity and a big reason for people's faith in Christ... There are no perfect people, there are not any people that even qualify as "good"

Christian doctrine carries no illusion that once someone becomes a Christian they become perfect. In reality, to become Cristian is to come to terms with your imperfection. It is still morally justified to confront sin in the community.