Why do we call some full moons "blue" when they're not?

This Sky & Telescope article attributes it to the Christian ecclesiastical calendar:

The ecclesiastical vernal (spring) equinox always falls on March 21st, regardless of the position of the Sun. Lent begins on Ash Wednesday, 46 days before Easter, and must contain the Lenten Moon, considered to be the last full Moon of winter. The first full Moon of spring is called the Egg Moon (or Easter Moon, or Paschal Moon) and must fall within the week before Easter.

At last we have the "Maine rule" for Blue Moons: Seasonal Moon names are assigned near the spring equinox in accordance with the ecclesiastical rules for determining the dates of Easter and Lent. The beginnings of summer, fall, and winter are determined by the dynamical mean Sun. When a season contains four full Moons, the third is called a Blue Moon.

This article traces the etymology of "blue moon:"

"Blue moon" appears to have been a colloquial expression long before it developed its calendrical senses. According to the Oxford English Dictionary, the first reference to a blue moon comes from a proverb recorded in 1528:

If they say the moon is blue,
We must believe that it is true.

Saying the moon was blue was equivalent to saying the moon was made of green (or cream) cheese; it indicated an obvious absurdity. In the 19th century, the phrase until a blue moon developed, meaning "never." The phrase, once in a blue moon today has come to mean "every now and then" or "rarely"—whether it gained that meaning through association with the lunar event remains uncertain.

Neither source mentions possible atmospheric phenomena that can absorb red light and turn the moon blue.

It seems the term blue moon has been around for over 400 years, but originally it just meant something ridiculous (akin to the moon is made of green cheese/pigs might fly/etc.). The fact that unusual atmospheric conditions may impart a blue tinge to moonlight is apparently not relevant. Over time, the meaning morphed from ridiculous to very rare.

In 1819 The Maine Farmers' Almanac came up with the definition cited by OP, and from then on, it listed "blue moon" dates every year. But the dates they list often don't even meet their own definition, which is somehow bound up with the Christian ecclesiastical calendar.

Insofar as it's a meaningful concept in respect of actual lunar cycles (which I don't really accept), we normally define blue moon today as any second full moon occurring within a single calendar month (i.e. - the first full moon must have occurred in the first few days of that month).

Blue moon refers to two full moons within the same calendar month. These are rare because the ion cycle of approximately 29.5 days usually occurs once within a 30 or 31 day month. The blue moon can appear during any season; usually about once every three years.

Obviously, it has nothing to do with the color, although dependent upon atmospheric condition, any moon can take on a slight blue tinge.