Does the term "agnostic atheist" imply that those who self identify as such should accept that it is reasonable for others to hold a belief in God or gods? This does not mean agnostic atheists would be obliged to find the justification given by every theist for their god belief to be reasonable. But we would at least, I think, have to acknowledge the possibility that their private reasons for belief in God or gods are reasonable for them. Do you agree?
The term agnostic atheist is absurd. It is dancing around acceptance of atheism as a reality. It is an abdication of reason. Sometimes it is hard to reach the decision to accept the reality and rationality of atheism for some people. It is a form of moral cowardice
To OP: only as mere possibility, yes, even if not strong. It might not need to be the atheist's business, if it isn't making relationships and dealings bad. In most cases we don't know how to "believe in" is seen. I thought a thing I gave the job title "god" was somewhere. I never assumed anyone would strongly want me to have the same concept as them. Insofar as there were overlaps these sometimes seemed interesting and sometimes didn't. We had no problem with atheist neighbours and they had no problem with us. I later mixed with the pushy type, and now I have pulled back out of that. When I was mixing with them I was far from a carbon copy of them and I wasn't doing their will much (though it was too much).
For all the close overlap between "atheistic agnostic" and "atheist" I don't think we should be taken as trolling or taunting anyone with any connotations. What contrasts agnostics from bad religion is our lack of absolutism (which fits mathematics). As agnostics we can be functional honest theists of any description and functional honest atheists of any description. Our scale of theology concept goes from zero point something infinitesimal, to infinitely near infinite. The people that had Edward Harte in their grip, are utterly scandalous. They had no justification to maintain that their interpretation of doctrine had any validity or genuineness. Atheists are utterly right to be suspicious of the quality of the line they are putting forward.
Of course we know, for our purposes, at what level god(s) don't exist and what we don't want to think of it / them. We are not agnostic as to our beliefs. This is about boundaries and quasi-indexicality. When others spout nonsense about their beliefs, we should either be wary for us, or wary for them, or not wary, on a case by case basis.
A thing that doesn't attract me to some people's version of atheism is an absolutism they borrow from bad religion. I would get on perfectly with Russell (though he is shaky about the ontology of Poseidon, one of my favourites). I think there has been an unhelpful rash of show-offy pieces about atheism from people not sympathetic to it, and I'm suspicious of the intent in pushing them. At the same time accusations against agnostics all along the scale smack of bad religion.
Actually, let's ask - why this question? What will the definitive answer to this question get you?
Why don't you self-assess, decide what YOUR beliefs and moral compass should be, and leave others alone to make their own decisions without second guessing their motives and intentions and putting words into their mouths?
Reasons that last only pop up when you dig down deep into cause and effect. 'Beliefs' that are on the way out often originate with one person e.g Bernadette at Lourdes, or a small group who travel with a controlling leader. Our beliefs spring up by large numbers of people coming together after NOT accepting what to do and what to praise. They do it because they think things out for themselves. Now all they need to do is find out how to politely say to religionists "You can those thoughts without any bad effect!"
I identify, first and foremost, as a nullifidian--a person who has no faith or religious belief. Faith is an unreliable reasoning process which acts as a virus. To quote Peter Boghossian, 'faith is pretending to know things you do not know.' All should be inoculated against the virus of faith. As far as religious belief goes, religions and their clergy, scriptures, doctrines and creeds are, in my opinion, without value and even harmful, and should be jettisoned from societies.
From that premise, if there were a god, it/she/he is irrelevant and I have no knowledge of it/her/him, and I most certainly have no belief in it/her/him. Lacking knowledge of a deity defines me as an agnostic, while lacking a belief in such defines me as an atheist. I don't really care either way ... I'm just a nullifidian.
I don’t actually care what anyone else believes, unless it hurts someone else without their consent.
Agnostic to me is the ability to not care about things that don’t matter to me, and prioritise the things that do: there’s a great freedom in that.
Sometimes others’ beliefs interest me, often these days, they don’t. Some beliefs I respect, others I find it very difficult to, but I try and get along with everyone as best I can.
The guy in the institution who thinks he is napoleon finds his bekiefs reasonable. It doesn't matter what we nonbelievers call ourselves. Believers believe and therefore find their beliefs reasonable. Users use them and either do not actually believe or have made themselves believe that there js a god who wants them each to have a orivate jet or two. What has any of that got to do with what we call ourselves?