Regarding reproducible evidence,
I agree that if something is repeatable and subject to controlled scientific experiment, it is likely to be accepted by science. That acceptance might be slower and more troubled if it contradicts too many strongly-held preexisting beliefs.
But I'm less comfortable with any suggestion that if events aren't 'repeatable' then they can't be real and must be met with sarcasm and ridicule.
I'm inclined to accept the possibility of one-off events (certainly one-off in our limited experience) that aren't repeatable on command or otherwise observed to repeat in nature. I remember arguing this point regarding radio emissions received from outer space on a single occasion, never to be duplicated. The origin of life and the big bang might be other examples.
Ghosts seem to be located midway in that spectrum. Reports of apparitions are common throughout history in pretty much all known cultures. Reports of their occurrance come very close to being cultural universals. I think that's fascinating in itself and perhaps worth more scholarly attention than it typically receives.
I'm most inclined to interpret them as subjective psychological phenomena. Photographs and so on seem to argue against that interpretation, which is why I find them interesting. I'm always interested in finding good convincing physical/instrumental evidence of ghosts and other 'fringe' beings.
But apparitions don't seem to be conjurable in a laboratory on demand. They happen when and where they happen. So they aren't repeatable in a strict bench-top sense, but may well be repeatable in the sense that supernovae are, where astronomers just have to wait for one to pop off.