>science in principle shouldn't treat them any differently than results about "regular" subjects.

That's the whole problem, as I understand it. If we are going to treat ESP research the same as research in other fields, we either accept ESP as real, or reject both ESP and other fields as deeply flawed.

Personally, I'm leaning heavily toward the second option. The methods in ESP are identical to methods in psychology, social sciences, etc, but not physics or chemistry. I'm just wondering where to draw the line. Maybe the whole method of statistical inference needs to be flushed? Maybe it cannot be saved by preregistration, publishing all the data, transparency and other bells and whistles.