Near-Death Experiences, And A Little Thinking About Extra Claims In This Textbook

It's a quite frequent idea that people would share similar experiences when they underwent situations where they "almost" died. We've seen such episodes in a bunch of films, and even learned some story of near-death experiences from family members or even ourselves. The world suddenly seemed static, and a life review of all the memorable times when we spent with the ones we loved, as well as a light through a dark tunnel came to our mind step by step.
According to the textbook, near-death experience (NDE) is an out-of-body experience reported by people who've nearly died or thought they were going to die. Giving a few illustrations about NDEs differ across persons and cultures as well as other facets, the authors generally alleges that those claims are extraordinary but without extraordinary claims. And though they didn't show absolute words denying NDEs and souls, readers can easily feel their contempt toward such phenomenon through some insufficient refutations and their fondness of materialistic theories even when both of them have little evidence.
And that behavior of belief perseverance can be a problem, especially making their critical thinking not as "critical" as they think they do. Before college, I've watched an online course of of Yale University. I still remember Professor Kagan's an analogy of near-death experience. He suggests that, if you go to the border of France, you can have an experience of what France is like (though maybe just a general glimpse), so why can you say that those people who have NDEs knew nothing about death because they didn't "really" die. That makes sense. And though I am not an idealist and I love science, I do worry that the materialistic current let our scientists trapped in such a confirmation bias that they try every possible materialistic theory and value them while largely overlook the evidence for idealistic theory because due to their nature they're regarded as not "falsifiable".
Here's a story my father told me. When he was on voyage to Antarctic as one of the crew before I was born, one night he suddenly woke with tears in his eyes. He dreamed that his grandpa, who brought him up when he was little, died and came to see him the last time. As the communication in China was not that convenient more than twenty years before, he simply marked the time when he dreamed of his grandpa. Finally when he came back, he asked his mother how his grandfather was, she told him that his grandpa had died for a long time. And when he checked the time his grandpa died, it is exactly the same day when his grandpa came into his dream and said good bye to him. You may say that this is anecdotal, or say that it's just a father who wants to show mystic toward his son, or you may refer this as just a coincidence. If you do, then you're not a scientist because you evade from things that you can't explain and deceive yourselves instead of facing them. And science should be not only all about finding the truth, but also introspect ourselves, eliminate flaws in thinking, to better serve this process.
And here comes the question: Is "unfalsifiable" meaning something is not able to be real? Any cautious readers of the book will tell that unfalsifiable only means that they are not in the Science realm and we thus are not going to examine them because they're not already part of science. But, if something is shown real even though their nature lets them not replicable or falsifiable so far, will our scientists largely ignore them and refer them to either invalid anecdotes or metaphysical realm that science will not pay attention to kind of deceiving ourselves? Science is not a government department, which is only responsible for this part or that part. It's supposed to examine everything that does exist and try to find "why and how". If anyone insists the border between science and religion, we who know a little world history will tell them that initially everything is of religion before science appears. After all, before we gradually accumulate former experiences and methods, how can whether the sun surrounds the earth or vice versa be testable?
It's just personal idea. Hope that they're not that wrong.