What the Romans did or did not believe is entirely irrelevant, as I doubt even the most ardent Society members think moonstone is made from moonlight.
The "Transylvania Effect" study - interesting that you should quote this one when you don't believe in gravity, as the abstract suggests it is the gravitational pull of the moon which is the root cause, not its light.
Crime affected by the moon: yes, but again no evidence at all that it's the light level which is responsible. You'd need to compare data from cloudy full moon nights and clear full moon nights, or from the waxing and waning phases (waxing moon should show more crime than waning moon, as more people will be exposed to it due to the earlier time of night it rises in the sky.)
Moonlight disease: not caused or even triggered by moonlight, according to your link. I would also request evidence that scarring and lycanthropy can be caused by moonlight, because that's kinda unlikely in my view.