Maybe it depends a bit on what one considers agnosticism to be. To me, agnosticism means allowing the possibility that, since we don't or can't know, therefore some specific thing might exist. If you were to be an agnostic about Xenu you would have, in some real sense, to allow the possibility that the Xenu story is true, and if someone else comes up with a story equally crazy, you'd have to allow the possibility that that one is true. If you say, "that's made up nonsense," then you're not agnostic, even if you realize you can't disprove the nonsense. To meaningfully say you don't know requires also that you don't judge.
I find it actually, functionally impossible to believe on demand. I can try to do intellectual justice to an idea, but it has to stand on its own. I cannot believe in something in order to study it. In fact, I cannot even conceive of how that is possible. In fact it sounds much like the escape clause that paranormal believers often use, that you can't judge a belief unless you believe it first.
Perhaps the problem is either that your understanding of what Agnosticism is, is faulty, or is not, then there is another way of looking at things but it cannot be referred to as strictly being agnostic.
You said this: "To me, agnosticism means allowing the possibility that, since we don't or can't know, therefore some specific thing might exist."
In relation to any specific god idea, - one can of course delve in and take a good look at what is offered and decide for a number of logical reasons that it is unlikely such a god exists, and choose to disregard that idea of god as being something which actually exists.
One does not have to also form beliefs that the god in question does not exist, or even necessarily get into arguments with those who believe that particular god exists, or does not exist.
One is still not making any statement of belief one way or another. One can say 'I really don't think such a being exists' but never know for sure one way or the other.
Also - on the idea of god(s) in general, one might decide the exact same thing, or decide that all the ideas so far are faulty - or they reflect far too much human vanity, arrogance, posturing etc to seriously consider, but one might also think that one can come up with or come across ideas which are far better ideas which one might consider god(s) are more likely to be like which are nothing much like the popular ideas abounding.
Any god ideas are just that. Ideas. It is illogical and irrational to believe in them. Some god idea(s) which are believed in are acted out and prove to be damaging for that and thus voicing an opinion of protest is the least one can do but even that can get complicated.
Some god ideas are confusing and contradictory. To believe in these ideas requires having to explain the obvious contradictions in a manner that shows clearly that they only appear to be contradictions - which can be part of the process of investigating (to require explanation from those who believe in these ideas) - to hear the explanations and see if indeed they are applicable or just ass-covering.
If just ass-covering then it is appropriate to disregard the idea. One does not have to position oneself within structures of belief in order to disregard and then argue from that position of belief.
