who knows if the god(s) they worship are real or not?
Nobody. They claim they do, but that's not convincing. How could they know their god exists? We can rule out many gods, but not all gods. Nor need we to justify atheism.
I am atheist and say "no", god(s) do not exist.
How do you know that? I don't consider gods any more likely that vampires or leprechauns, but I also don't say that they don't exist, because I have no observation, experiment, or algorithm that can rule them out. Nor need I. But my language is not that they do not exist, but that I don't believe that they exist because I have no reason to. Why actually say that I know that they don't exist when I don't need to and can't justify it. It's just another leap of faith.
the lack of falsifiable evidence
I've never understood just what you mean by this term. How is evidence falsified? Yesterday, I asked the same question of another poster who referred to verifiable evidence. Claims can be falsified (or supported) with evidence. That's what Popper meant by a scientific statement. It's the statement that is falsifiable or not, not the evidence. Is that what you mean?
can you provide the main reasons for your belief/unbelief in god(s)
Same as yours. I'm a critical thinker, meaning that I'm also a skeptic and empiricist, which I consider an asset and a defense against accumulating false beliefs. Incidentally, I use the word unbelief these days to represent my agnosticism and disbelief to mean that one considers a claim is false. It's not standard usage, and I have to define the words explicitly before using them that way, but it's a useful way to think. If you have two distinct concepts and two distinct words, why let both words have both meanings when we can assign them 1:1.
If one experiences a god or god, then in that person's reality, god(s) exist.
True, but does that matter to somebody else? I've had experiences that I attributed to the presence of the Holy Spirit, then later reinterpreted as endogenous spiritual states. You might say that God went from real to an idea when I made that transformation. God went from something that existed outside my mind and was being experienced by it the way it experiences lights and sound as evidence of the existence of something outside of the mind, to a misunderstanding of a feeling generated by a brain state. My definition of reality includes what really exists and only that. Yes, the idea of a god exists, but that's not the same as its referent existing.
If god(s) didn't exist, then neither would this forum.
So then you're offering RF as a proof of gods?
Behavior resulting from the experience of X is evidence of X.
Perhaps to the one having the experience, but what behavior in others changes a false belief that they might hold into a correct one? We're reminded of the Christian martyrs who died often horrible deaths for their beliefs and asked to believe that that is evidence that their beliefs were fervently held, which I can agree with, but not that they were correct. There were dead people in Jonestown, Waco, and Rancho Cucamonga who fervently believed that Jim Jones, David Koresh, and Marshall Applewhite were telling them the truth, but their behavior doesn't convince us that their beliefs were valid.
"Real" by what definition?
An empirical one. There is no value in calling something real that cannot be detected empirically, meaning, cannot affect things that are known to be real.
Why should your opinion trump anyone else's?
Because it's her opinion. Mine trumps everybody else's as well for me. Even when I defer to experts, it's my opinion that that is the best course of action even if others disagree. I see an element of gaslighting in all such comments that ask one to suppress his own judgment and substitute somebody else's. It's the central message in Christianity, and failure to substitute its reality and morality for one's own do is called rebellion, hedonism, or wanting to play God. Be humble, we are told, and stop asserting your will. It's also your message with your frequent referenced to scientism - that the naturalistic position is too myopic and that reality is something different than what the recalcitrant empiricist sees.
I am hoping that by now you're beginning to see the circular foolishness of asking the question "is God real?" when we don't know what "real" is or is not. Or what God is or is not.
You might not know what real is, but I just gave you a concise definition that includes a test. And the question is very useful. It forces one to examine more closely what one means by both God and real.
"Belief" is not a requirement of theism.
Sure it is. Theism is a category of belief. And it need not be justified belief, either. Any belief in gods is theism for me. I understand that others use the word differently.
the nonsensical answers that you do get will serve to bolster your otherwise unfounded atheism.
No position but agnostic atheism is justifiable if one is an adherent of the laws of critical thinking and of evaluating evidence. Any other position is guessing.
I would like to add the idea of mystery to the idea of the universe. I think that for a lot of people, the mystery of our existence is both scary and wonderous. Significantly so. Which is why we feel the need to personify it, and hold that personification close to our hearts and minds like an invisible friend.
You might need to personify it, but I don't. My friend is nature, and it's not invisible. My spiritual life results from a direct relationship with nature. That warm feeling of connection, safety, and belonging often accompanied by awe, gratitude, and wonderment can happen while gardening or playing with my dogs or hearing a rapturous passage of music or gazing at the night sky with understanding, and never makes me think of nature as a person or makes me want to give it a name or start performing rituals to it. I simply don't need to inject more into any of that to consider it sacred, by which I mean divine less gods.
Strip the gods out of all of this, I say. They're not too harmful if they are a panoply of nature gods, where they just become symbols for various aspects of experience. The real trouble comes when people start extracting the sacred from nature, and sticking into gods that are separate from nature, especially gods that don't have much respect for our world and give man commandments and received moral codes - the antithesis of spirituality as I have defined it here. That's not your problem. You seem to have avoided that. But be careful of anybody coming to you telling you what God is and thinks and wants you to do. I think you already know that.