i dont think breeding timing is influenced by moon phase what so ever. The moon phase thing just doesnt add up. If the moon was the trigger for breeding the timing of fawn drop would have substantial swings from year to year,which doesnt happen.
Moon phase may however have an impact on the timing of deer movements within a given day...but i really have not seen a strong correlation to that in own personal observations.
There is a ton of research by lots of state agencies that use fetal back dating of road killed and hunter killed does that put the period of peak breeding into the same 5-7 day period year in and year out for that given state or location with in a state.
But it all depends on what someone means when the say "the rut". I think most people use "the rut" to actually describe a very wide range of breeding behaviors. The rut really has several different phases that overlap and ebb and flow, but follow more or less the same progression on the calendar every year for a given area in the northern 1/3 of the country. For me, i usually see the first daylight scrape or food plot pic of a mature buck around Oct 20th through October 25th. Then by about Halloween, i'm not only seeing more pics of mature deer on their feet, but i'm seeing them with plenty of shooting light on the horizon driving around or going to and from work, etc. Things pretty much only pick up from there as November progresses. Our early archery season ends around November 15th every year. In most years the last 8 - 10 days of our season are the best in terms of rut behavior, then by time the season is over peak breeding is going on and buck sightings drop of for few days while they are busy with the does.