what is the most important aspect of the interaction between belivers and non believers

[TM99]

228. Actually he does.

The proposition being considered is this - is there a god or gods.

The theist accepts the proposition as valid and answers 'yes'. Their 'belief' then may rely on personal or subjective experiences and/or emotional faith.

The agnostic accepts the proposition as valid and answer 'maybe'. Their 'belief' then may rely on the same things as an atheist (lack of empirical evidence), however, they remain open to experiences for a variety of personal or subjective emotion and or rational reasons.

The atheist also accepts the proposition as valid and answers 'no'. Their 'belief' relies on the sole question of whether there is empirical evidence and a falsifiable theory. Of course the later is the by-product of scientism and the new 21st century New Atheism.

So yes, all three accept the proposition as valid. As a atheist, you may say that you lack 'belief' in a deity or the religious dogma, theology, etc. that supports such an expression, but you do accept the proposition in order to answer it in the negative. Generally speaking, an atheists 'ideas' of god or gods is based on what religious culture they were exposed to as they psychologically developed.

Everyone has a personal set of beliefs - a philosophy of life. Generally speaking it starts from this proposition and expands from there. Even my ignosticism supports a 'belief system', it simply doesn't start from the above proposition which I firmly reject. As an atheist, you certainly have beliefs. They may be negative ones such as accepting the proposition and then rejecting religious dogma, deities, etc. They may be positive ones such as blending secular humanistic components. But to attempt to say that 'atheism' as individuals actually use the word is completely without 'beliefs' is bullshit. I could clearly show from posts you have made that your 'atheism' definitely has 'beliefs'. Are they the same as all atheist's? Some yes and others definitely not. But the same is true for those who call themselves religious.