In my opinion, the issue is that what is meant by "ghosts" is unclear. I am not remotely "woo", I am a rationalist.
Science has paradigms. During previous ones, if someone had told you that snakes can sense heat on the sand from animals that have moved across it hours earlier, you might have said that is impossible. Now, we know that snakes can sense infrafed.
Previously it was a mystery how some birds managed to navigate their migrations of thousands of miles. We know now that, in some cases, they can sense the magnetic fields of the Earth.
Much other animal behaviour remains completely inexplicable. Yet we observe it, so there must be a rationale that is, as yet, obscure to us.
Humans have five senses because these are the ones that happened to evolve to best assist our survival in our particular environment. That does not mean that anything which exists outside of these five senses, or their range, does not exists. Otherwise we'd have no need for X-rays, for example.
To me, it would be the epitome of arrogance and stupidity if we were to assume that our current science tells us all there is to know. We are, after all, just a clever type of monkey, and we should not forget this. Einstein for example proved that Newton's physics was correct but within the limited bounds of its assumptions, and not applicable more widely.
I do not believe that there are "paranormal" phenomenon. But I do believe that our science is not advanced enough to claim that we can explain everything or that anything that our current science cannot explain doesn't exist. If that was the case then all scientists could retire. The entire purpose of it is to investigate and understand and perceive things that we cannot necessarily perceive directly without instruments that measure things beyond our field of vision etc.
There is also significant support from physics for the theories that there may be multiple dimensions that we cannot perceive, and that time is not linear.
I would also add to this, that the idea that what you see and perceive directly is "real" is a can of worms in itself. What do you mean by "real". A large percentage of matter is empty space yet your table does not appear to you to be transparent. Your brain interprets the sensory information it receives and creates your image of the world. There is no such thing for a human as a direct perception of what exists. See my username: magenta does not exist. Well, only in your mind.