I think that currently society is too polar about this issue. A lot of so-called pseudoscience have a lot of anecdotal evidence that should be taken into consideration and don't have a lot of science to deny them. On the other hand a lot of them do have that so there is an issue where there's a lot of people who believe a lot of different pseudosciences because some of them genuinely seem to have results but the people who go explicitly by scientific research sometimes can group all of these together. For example, homeopathy is obviously bullshit, and there is a ton of scientific research that shows that. But, for example, a lot of Chinese medicine, which has no scientific backing, does seem to have a lot of anecdotal and historical evidence that suggests that if science does look into it, they might find some actual results.

I don't know what lunar effect is, but the description you gave sounds very plausible. Like, why wouldn't a full moon affect the behavior of humans and other animals? How it affects them? To what degree? Sure, that's debatable. But generally affecting them, that sounds reasonable. It's a significant change in the night. It lights up the night more and It wouldn't be a stretch to assume that some animals might use it as time management indicators that might relate to biological cycles.