A blue moon isn’t blue:
A blue moon can refer to either the third full moon in a season with four full moons, or the second full moon in a month.
Most years have twelve full moons that occur approximately monthly. In addition to those twelve full lunar cycles, each solar calendar year contains roughly eleven days more than the lunar year of 12 lunations. The extra days accumulate, so every two or three years (7 times in the 19-year Metonic cycle), there is an extra full moon.
The Middle English word belewe can mean blue or betray:
By the 18th century, before the Gregorian calendar reform, the medieval computus was out of sync with the actual seasons and the moon, and occasionally spring would have begun and a full moon passed a month before the computus put the first spring moon. Thus, the clergy needed to tell the people whether the full moon was the Easter moon or a false one, which they may have called a “betrayer moon” (belewe moon) after which people would have had to continue fasting for another month in accordance with the season of Lent.
The moon may appear literally blue when smoke or dust clouds the sky, as after a major forest fire or volcanic eruption — which only happens once in a… never mind.