Moons used to be on outhouses, so moon is for sitting, and you can pee outside so sun is for standing.

Or maybe women have cycles like the moon so that's womens.

Maybe girls are hot so they go in the sun, and men are creepy so they go under the moon.

Or maybe it's not men and women at all. It's hot people and creepy people.

Or maybe one is always closed for cleaning, so you use the sun during the day and the moon at night.

Maybe they're really into vexillology and the sun is for Japanese people and the moon is for Turkish people.