Interesting topic.
A few things about real moonlight that are very different from the shocking bright blue lights that people run and call moonlight:
1. real moonlight is very, very, very dim underwater, even during the full moon. Go SCUBA diving at night during the full moon and turn off your lights. Its nearly pitch black.
2. real moonlight doesnt come on for a few hours after sunset each day. The timing of moonrise doesnt line up with sunset, its on its own cycle.
3. moonlight is much more white than blue.
Does moonlight affect anything? Well, a few years back I simulated moonrise in my old experimental tanks and induced planulation (release of asexually produced larvae) by Pocillopora the morning after the full moon for 4 or 5 months in a row. Just like in nature, moonlight appears to affect at least some biological processes in the aquarium.
Not sure if we have evidence of harm yet. The cases that make me wonder about possible harm are the tanks with lights on 24-7 (white at day, blue at night). Thats gotta be weird, to evolve in a 12-12 light cycle then suddenly go to a 24 on.