What's the main logical basis that is put forth by those Christians who don't believe in the existence of God? What's the main logical or doctrinal basis that is put forth by those Christians who don't believe in the existence of God? I mean, in the Bible Jesus spoke of God the Father many times, so how do they logically explain their belief that God doesn't exist?
As an alternative to "Christian Atheism" as a belief system, there is another interpretation here of a Christian who does not believe in God, which is the "cultural Christian". This was reminded to me by a comment on the question referring to "Jewish" as both the adherents and / or the society - but is has been identified that this is very genuinely the case for Christianity too. This obviously is not based on a scriptural position, but on society and observation; there really are a large number of people who will identify (when asked in passing) as Christian, by which they mean (typically) they have been raised within Christianity, but don't really believe in it as such (and don't typically attend a church or worship, except maybe things like "saying grace" at mealtimes through habit and expectation).

This may be tied to the fact that to say "no, this is not what I believe, and I shall separate myself from it" can sometimes take a lot of effort and energy, jeopardise friendships and relationships (and humans are social creatures) and prospects (perhaps impacting business relationships). It can also cause friction within a family, etc. I can fully accept that it may be a lot easier to just "go along with", since that takes no effort (not even church attendance etc) - especially if their stance one way or the other on the matter is not of huge importance for them (compared with, say, more pressing needs like feeding the family and paying the bills). There are also sometimes additional factors if they want to get their kids into a particular school (alarmingly common), where rocking the boat may cause complications.

So - looked at from that perspective, the cultural Christian (in reality, not a true believer) is a very real phenomenon. This is not, however, a Biblical basis - it is, simply, an observation on the complexities of modern society.

(removed "modern", as there is no reason to suppose this is in any way new)