In essence, the paranormal is real, but you will never be allowed to prove it (or allowed to undeniably prove it).
I believe that there's a simple reason for this. Robert Monroe, one of my prime inspirations and a giant in the paranormal field who sought to apply objective, rational analysis to the experience of OOBEs, posited in Far Journeys that:
the conditions of entering physical life as a human are relatively strict. It is as if a detailed agreement is entered into. First, the energy form must agree that time-space truly does exist. Without this agreement, it is impossible to have primary human consciousness. The energy form must agree that there is a time, such as the 1980s or any other time frame by earth reckoning. It must be agreed also that there truly is a planet earth designed and created in the form that it is. It must further agree that consciousness expressed as a human has certain characteristics and limitations.
This "contract of human experience" is alluded to in many other esoteric writings, and I believe that it is valid. We are born under contract to believe unquestioningly in the inviolability of physical existence and physical laws; it is unconscious but also absolute. The aversion toward any phenomena that seeks to undermine this perceived physicality is so profound that most of us "tune out" paranormal phenomena; when our filters fail and the paranormal manifests, we have several responses: we debunk it; we explain it away; or we ignore it. To embrace the paranormal seems to violate some unconscious taboo that threatens the nature of our physical existence.
I believe, however, that such laws are not immutable. Some writers (Michael Newton, Jane Roberts, and others) believe that the coming century will see a loosening of the strict physical contract. Humans born in this century will be born under a looser contract, and what now is viewed as paranormal may become the new normal. There's a lot of anecdotal evidence that this is already happening. Rather than entering into any sort of hokey "new age," I think simply that we are entering a new normal. And I welcome it.