I don't think atheism and theism are true opposites. There are opposing ideas in them, but they're not truly all opposite in everything... And I don't think belief is discontinuous either. There are shades or different levels of belief. You can hold something for more or less likely, and maintain different levels of belief.
Important points.
What happens to belief when it is a probability? "I'm going to flip a coin, do you believe it will be heads or tails?"
Or with an apophatic theologian 'Do you believe god exists?' 'I refuse to be drawn on the question of whether or not god exists as I don't consider existence a classification that can be applied to god'
In my OP I mentioned Meister Eckhart, who Fritz Mauthner considered a true atheist because he refused to accept that it could be stated that God existed (Mauthner's atheism was related to his critique of language) .
Eckhart stated: "Our salvation depends upon our knowing and recognizing the Chief Good which is God Himself. I have a capacity in my soul for taking in God entirely. I am as sure as I live that nothing is so near to me as God. God is nearer to me than I am to myself... Thus must the soul, which would know God, be rooted and grounded in Him so steadfastly, as to suffer no perturbation of fear or hope, or joy or sorrow, or love or hate, or anything which may disturb its peace... the soul should be remote from all earthly things alike so as not to be nearer to one than another. It should keep the same attitude of aloofness in love and hate, in possession and renouncement, that is, it should be simultaneously dead, resigned and lifted up." (Doctrines of Meister Eckhart - Wikipedia)
Now Eckhart was clearly a Christian who refused to make a comment about God that he disagreed with (God exists).
Does he fit neatly into an atheist/theist dichotomy though?
To have a word that fits both his and Richard Dawkins' beliefs means that it must be a very vague concept and one in which we must be prepared to view with a fair degree of nuance.