I believe it's possible to be sensitive to the paranormal, but without any knowledge of this sensitivity, you would tend to shrug off the phenomenon. For example, when I'm in a haunted place I'll sometimes feel a disoriented sensation. In the past, before I became aware of paranormal phenomena, I would have that sensation and not realizing what it was, I would just shrug it off as one of those random events. Last year I learned that paranormal occurrences can be "felt" in certain ways, and then I had the disoriented feeling while dining in a haunted restaurant. That's when I made the connection, and realized I can "sense" if a place is haunted, to some degree.
Much like a blind man experiencing sight for the first time, it's hard to understand what you're feeling without learning about it. Sure, everyone is raised to understand the normal five senses, smell, sight, taste, hearing, and touch, but the "sixth sense" is often downplayed. "There's no such thing as ghosts", your mother tells you. I spent 36 years of my life not knowing that "disoriented" feeling was caused by something my mother told me "doesn't exist".
I bet if society were more open to the paranormal, more people would experience such phenomena, and know about it.