For "unconventional science" read "mumbo jumbo". Parapsychology does not qualify as science, unconventional or otherwise. It only qualifies as quackery and bullshit.
Because it's been rebuked by research. Conducting that research, however, is what science is all about: test claims to see if they're correct.
Heck, you could do parapsychology research today and, as long as it's properly conducted, it would be science. It's unlike such experiment would do more than confirm what's already known, but that doesn't make it "mumbo jumbo".