I think we can all agree that there is a lot of "weirdness" that gets attributed to celestial phenomena.
Not too long ago people used to think that comets were harbingers of godly doom. ( even in the freaking 90's with those Nike shoe wearing Heaven's Gate peeps).
There is a definite crossover between superstition, religion, and pyschology.
Meaning, we have this superstition of the big bad full moon.
We then, have people that do ritualistic things during a full moon,
We then, have psychologists that try to help all these people.
The gravitational pull of the moon does effect our tides.
This much we know as fact.
Further than that?
Nothing has been proven empirically that the moon effects our brain chemistry.
Because that's what our brains are.
Chemical machines.
For something to "mess with them" , it would have to be something directly attributable to our neurological chemistry.
Drugs do this, genetics do this, as can certain environmental factors.
But thus far, we haven't been able to equate the slight gravitational pull of the moon, into real chemical fluctuations in our minds.
We know gravity can affect our bodies , but it has to be of a certain force for it to do so.
The full moon wives tale , is a bit of self-fulfilling prophecy and a bunch of other possible sociological, spiritualistic, and psychological scenarios that cause us to make mountains out of nothing.