Actually, lunar cycles do affect quite a few people's behaviour, hence the word "lunatic" to describe people with what used to be preceived as madness. Ask any midwife about when women's waters are most likely to break and the answer will be during a full moon.
Let the doubters doubt. Let those who believe believe and let those who just need a bit of help organising their time follow the calendar as they wish but let's be clear. This is not gardening by moonlight. This is gardening according to the cycle of the moon as it orbits the earth each month.