Beltane is a traditional Lunar festival, one of four marked by fire, as recognized by Celtic Heathens and Pagans:
-Samhain, Imbolc, Beltane, Lammas
-Winter Nights, Disting, May Day, Freyfaxi (Germanic Pagan / Asatru)
-Dziady Jesienne, Gromnica, Tydzień Rusalny, Domowy (Slavic Pagan / Rodnovery)

Today, all these observances have been centralized on the Gregorian Calendar, or the de facto calendar used to “inform” and “agree upon universally” all dates (civil or social). It is named for Pope Gregory XIII, who introduced its use in 1582 CE. Its purpose was to “stop the drift of the calendar with respect to the equinoxes and solstices”, and to affirm that the heavens belonged to the Christian god alone:

Lift your eyes and look to the heavens:
Who created all these?
He who brings out the starry host one by one,
and calls them each by name.
Because of his great power and mighty strength,
not one of them is missing.
-Isaiah 40:26

Indo-European and other pre-Christian tribes, all observed the heavens – from lunar phases to longest and shortest days, from meteor showers to eclipses – and there is ample evidence to suggest there were trained astrologer-priests who marked these times for the benefit of their folk.

In the West, many know that this is the year 2017 Common Era, yet there are entire countries and peoples who are either dual faith or have dual reckoning. Such as:
-Hebrew Calendar, the year is AM 5777 (Anno Mundi [Latin], for Hebrew ‘Creation of the World’);
-Chinese Calendar, the year is AH 4714 (Anno Huangdi);
-Hindu Calendar, the year is 5119 YS (Yudhishthira Samvat); then, notably,
-the earliest known lunar calendar comes from Mesolithic Scotland, dated to 8000 BCE

Does it make a difference if Pagans today celebrate Beltane on May 1st or May 5th?

I think it does. For me, when the calendar became ‘universal’ – established by the Catholic Church, and recall that ‘catholic’ means ‘universal; universal cosmos’ – it took away a large portion of the original folkway (the ‘way of one’s folk/family’). For example, if those who seek to reclaim, and/or live their life in accord to the Old European Folkway, where to follow one of the calendar examples above, then they ‘forget’ that the Oldest Lunar Calendars and Identification of Constellations, are found in France and Germany, dating from the Upper Paleolithic; and that these represent mathematical computations for annual moon cycles, the ecliptic, solstice, and seasonal changes on earth.

According to the archaeological record, human recognition and tracking of the stars dates to Europe, 32,000 BCE. This is the same cultural group that left us the Venus of Hohle Fels (Baden-Wurttemberg, Germany), the Lion Man figure (Hohlenstein-Stadel, Germany), the Sorcerer cave art (Montesquier-Avantes, France), numerous carved ivory figures of mammoths and horses, bone and antler spear points and arrowheads, and a bone flute.

Further, and though considered inconclusive, there is the Aurignacian Lunar Calendar, which could be an example of a compact and portable lunar calendar carried on long hunting trips and seasonal migrations.

Hunting herd animals is arduous and requires hunters to travel and track horses and ibex, mammoth and bison, for weeks at a time. Calculating moon phases and seasons of the year requires mathematical calculation; and this science is not just recording the movement of stars and constellations, but the multi-tiered realm of the mysterious cosmos. Animals Below follow the Stars Above, and so time passes, becomes predictable to a degree, so that what is objective becomes part of human awareness, consciousness even.

Many today have lost track of the passage of sun and moon; many even have forgotten that the word month come from Proto-Germanic *menoth-, then Old High German manod, and Old English monað, all meaning “moon”. From full moon to full moon, plants, animals, even humans, follow the churning heavens overhead. Plants and animals remember .. it is humans who have lost this wisdom.

Knowing the moon’s phase and season meant that hunts could be organized, that seeds could be planted, and crops harvested; that tribal gatherings could be organized over vast distances, and that, literally, every aspect of life could be marked. As it is today, on a Christian model.
Personally, I don’t want to follow the Saint Days (St. Patrick or St. James), Epiphany or Pentecost, Holy Cross or the Assumption of Mary. These are not my folkway. I am more connected when observing the Wax and Wane of the Moon, of the Equinox and Solstice dance as clearly highlights the seasonal tides, and of the Between Times. These rythmes of n/Nature and Nattura, of hunting and planting, are both external and internal. Akin to the ancient Time Keepers of yore – the Seidfolk and Sages, the Magi and Astrologer-Priests, the Wearers of Gold Hats and Bronze Age ‘Lords of Time’ – all from the wondrously diverse cultures of Old Europe (and beyond), my inner Wyrd Consciousness will follow that stars as a river that ebbs and flows with the earth around me. And when I follow that course – marking the dates I consider Holy Days (‘holidays’) – my soul ever finds its True North, which is the certainty of authentic and ancestral self.

Would You Know More, And What?

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Beltane and Maypole celebration, 1917CE, Wisconson, United States