So, is there adequate reason to believe that the four so-called "Celtic fire-festivals" (Imbolc; Beltaine; Lughnassadh; and Samhain) are derived from ancient pagan festivals?
The February, May, August, and November crossquarter days, each located very nearly equidistant around the year fall in the middle of each of the year’s solar/astronomical quarters halfway between each solstice and adjacent equinox. The set of names for these we as Neopagans are most familiar with is the set from the old Irish chronicles: Imbolc, Beltaine, Lughnassadh and Samhain ( a few citations for these are found in documents over 1000 years old). Unlike the crossquarter days, the solar "quarter"-days are often uncredited or overtly denied by so called “Celtic Studies” authorities and Neopagan Reconstructionists as being irrelevant to the pagan Celtic calendar.
This system of crossed-quarters on the year's wheel implies that most likely there was in this region of Western Europe 1200 years ago or more:
(a.) a roughly correct knowledge of the number of days in the year;
(b.) a roughly correct knowledge of the definitions and dates of the two annual solstices and the annual equinoxes half way between them.
So when we find the folk calendar of Western Europe and the British Isles in particular further equally subdivided by these four crossquarter days, it becomes hard to deny the astronomical/solar derivation of the crossquarter days from the solstices and equinoxes ("quarter-days") between which they are so symmetrically framed. Yet most Celtic Studies authorities and Celtic Reconstructionists continue to discount the role of the role of solstices and equinoxes in the structure of the Celtic folk-calendar...
Oddly though we do have evidence of the solstices and equinoxes being very important in the concerns of the Christian church of the British Isles and these sources place them as significantly predating the oldest Irish crossquarter feast references, the sole references which the Recon's rely on as being evidence of the feasts' "pagan" derivation. Accurate astronomical knowledge was, at the least, critically important to the early British and "Celtic" Christian church in this period due to their obsessive quest and battle with Rome for fixing the "correct" date for Easter*. The date of Easter cannot be derived without a clear and accurate knowledge of the date of the March Equinox. By the time the 4 equi-distanced crossquarter feasts showed up in the Irish stories, the four quarters of the astronomical year framing them were already old news to the church-fathers of the British Isles and Ireland. Our oldest Irish stories mentioning them are several hundred years younger than our well testified evidence of early Christian calendar-making (quarters-fixing) astronomy.
So, we actually don't have any textural reason to insist that the so-called "celtic fire festival" crossquarters were actually a pagan tradition, since Christian calendar making needs had already framed them in place. For them to be adequately (ancient-) "pagan" we'll need to look for something more than what the Celtic Reconstrucionists have been taking for granted as enough.
All I can offer in defense of the Recons' position is:
"Absence of evidence does not constitute evidence of absence."
* see "De Temporum Ratione" (On the Reckoning of Time) by the Venerable Bede, (8th Century CE)