This is a profoundly irrational position to take. I understand it, because I also held it at one time.
The definition of science is:
There's that interesting word sitting right there... observation. Observations are in fact science. It is the start of science, i.e. the scientific method:
You are slightly correct that there hasn't been a lot of systematizing the observation which leads to the rest of the scientific method not being engaged. This is also my point. However, this is far from being universal.
Ray Stanford did this with Project Starlight International. Chris O'brien is starting this with his SLV Sky Camera Project. It is possible.
But to discount observations because they don't fit in with your worldview is the opposite of science. Whatever is happening is likely one of the most important things we will discover in human history. Even if it has nothing to do with aliens.
Because it's either us, or not us, or a combination of the two. And any of those three possibilities will likely change our view of ourselves and our place in the universe - because these experiences are part of the human experience, and always have been.
Think bigger. There are liminal spaces between 'they're all lying' and 'there are objects that I could hit with a rock with aliens in them.'
My experiences are not profound. They are not unique. I have never been given a message or meaning for anything. My background is math and science. These have troubled me since I was a child because I should not have had these experiences, and yet I have. Some have also been shared by trusted people, so I can't just be deluding myself. And yet they are discontinuous with the rest of my reality.
To ignore them because they don't fit with my world view (pretty classical empiricism) would be akin to astronomers ignoring planetary motion centuries ago because the stars aren't supposed to move.
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