1) You are extending your personal experiences into others. The average theist experience is not about recognizing the possibility of the supernatural and trusting in that possibility. That's your theism experience. That's your narrative. A lot of theists are absolutely certain that the supernatural exists, it is NOT a mere possibility they are trusting.
Almost none. In fact, only the 'crazy' ones. Some religions like to push on this idea that doubt is sin, or whatever. But I can honestly tell you that nearly every theist doubts. A lot. Because they are aware that 'God' is a cognitive possibility, not a physical fact. Over time, and with practice, they may get better at ignoring their doubts, and thanks to religion they may learn never to speak of it, but that doesn't alter my point, any. They have doubts. And they are choosing to trust in the possibility that their idea of God is true, regardless.
2) A LOT of atheists and physicalists recognize that God might exist. Neither of those positions entail being closed minded about possibilities. They merely entail that God is not part of their worldview.
So they say when directly confronted. But when you engage in discussion with them, you very quickly discover that they do not believe any gods exist, because according to their materialist way of thinking, there is no objective physical evidence of any gods. And, of course, what does and does not exist, by their reckoning, is defined by "objective physical reality". So although they claim they understand that God is possible. Nothing in their philosophy will actually allow for that possibility.
3) Atheists' arguments are of no consequence to theists because atheists' arguments concerning the supernatural is mostly about being skeptical, and skepticism is not for everyone.
Everyone is skeptical. And everyone is faithful. All that changes are the criteria and the objectives.
4) Recognizing that the supernatural exists alongside the physicality has absolutely nothing to do with "perception is conception, and therefor reality is an idea".
The former is an example of the latter. Awareness is not required.