Americans don't want an atheist president

That's not streching things, it's the definition and how it's used.

Read the very beginning of that wiki for the definition. Disregard the rest, at least as far as defining terms is concerned. Everything mentioned on the page actually discussing "agnostic atheism" is straight from Dawkins or the flying spaghetti monster. There are more than enough counterarguments for both of those straw men, the former personified and the latter figuratively. As I said, I know atheists want to claim agnosticism as a philosophical defense, but you can't have your cake and eat it too. There is no meaningful distinction between the definition of an atheist and what you call an atheist agnostic. A belief (which is unsupported by its very definition) that there is no god, tied to agnosticism, is somewhere between a logical contradiction and meaningless. To be agnostic, one cannot believe that they know whether there is a god. They cease to be agnostic if they come to that knowledge. Doubts are not the same as agnosticism. There's a difference between a lack of belief in presence and a belief in absence.

The way many people talk about this can be really misleading, people act as if matters of belief are completely separate from matters of knowledge. What you know in many aspects defines what you believe.

Whether or not Christianity completely or partially refutes all other religions isn't really relevant here - the point is that more or less all religions is incompatible with some other religion, and therefore you don't believe in that other religion.

It's exactly the point. The extent to which Christianity differs from any other faith is less than the extent Christianity differs from atheism. That matters when you're talking about why nearly a majority of people in a majority Christian country don't want an atheist president.

No, it just means you don't believe in any god(s). You don't deny that gods exist, you just don't believe that: Atheism is an absence of belief that any gods exist. It's a definition, it's not really anything to discuss.

There is an important difference between "I don't believe in a god" and "I believe no god exists" that is completely muddled if you define it that way. (the former I'd call null or irreligious and the latter is atheism). The philosophical difference is essentially as large as the gap between "I don't believe in a god" and "I believe god exists."

It's completely reasonable to not discuss it, because people could be bullied, teased, lose jobs, get thrown out from home, and so forth because of their beliefs. They may also understand that discussing this to people who believe otherwise won't have any effect because they've tried it earlier, or they just simply don't have time to discuss it.

All I was saying there is that I don't find it unreasonable to want to discuss your beliefs with people who don't share them, especially if you think someone disagrees with you in such a stark way. For a lot of people it's practically irresistible. I don't "blame" atheists who think religion is a plague, I just want them to be rational and consistent about their beliefs, which is more or less their main attack on religion.