In this case, rather than not possible, it’s here because we’d rather not promote pseudo-science. Science has repeatedly found the moon has no effect on human behaviour.
In this case, users are welcome to track whatever they like with custom tags, and we don’t claim that these tags have any scientific backing — we can’t, because we don’t know what they are, because they’re user-generated.
On the other hand, adding an attribute specifically for tracking a particular phenomenon means we’re explicitly giving weight to that phenomenon and its validity in affecting behaviour — otherwise why would we have added it?
So that’s why we won’t be adding it, but you’re welcome to track your own “full moon” tag and see what you find.