Let's Listen In
I have already refuted the non-neutrality claim. Why are you reiterating it? An atheist’s disagreement in this context, if biased at all, is certainly not less neutral than the claims with which it disagrees. So your accusation of “not neutral” is hollow.
I have already refuted your attempt to paint an atheist’s disagreement as an attempt at “moral authority”. Why do you continue to claim it and reword it?
The Pope: “Look! It’s God!”
Me: “No. It’s not God. It’s just a flower.”
The Pope: “No. God made that flower. And since you are atheist you can not disagree with me without making a moral judgment, which is contradictory for an atheist.”
Me: “My disagreement that a flower is not God is not a ‘moral judgment’.”
The Pope: “Yes it is, yes it is, yes it is! NA NA na na NA NA!!!”
That dialogue is a total strawman, at least for me. I do not and would not argue like that as a Christian theist. I think you're just tying to make fun.
To prove my point about the non-neutrality of disagreement, let me illustrate my own conversation:
[At a public gathering, outside the White House]
Chaplain: "Let us bow our heads in prayer to the triune God."
"Atheist": "Wait! Why should we all be told to bow our heads in prayer? There are some of us who don't believe in 'the triune God.'"
Chaplain: "You don't have to bow your head, if you don't want to."
"Atheist": "Why should we even hear people pray to an invisible guy in the sky?"
Chaplain: "Well, you can step out for a moment if you are offended by the public acknowledgment of God."
"Atheist": "Why should those of us
leave who don't believe in God?"
Chaplain: "Do you have a problem with public prayers to God?"
"Atheist": "No, but I don't agree that we should all have to listen to a person pray to something which doesn't exist."
Chaplain: "Why do you disagree?"
"Atheist": "Because there is no evidence for God. Religion has led to more wars than anything else. Science shows us there is no God. Humans can be moral without God."
Chaplain: "So, we should stop praying because your beliefs prove there is no God?"
"Atheist": "..."
That is essentially where the reason behind the disagreement comes into play. In the reasons given, the "atheist" shows his foundational beliefs which claim the moral authority for why there should be no prayer to God. His reasons given are not neutral, but they are very against his perceived atrocities of religion to God. They enact his disagreement to the public acknowledgment of God.