I don't think a thinning "veil between the worlds" has any historical connection to Druids, Celts, Banshees, or Leprechauns. It seems to have everything to do with 19th century romantic mysticism.

A survey of probable sources traces the phrase itself back no earlier than the tortured syntax of Mary Jane Serrano's 1883 mystical poem "Destiny," where it has nothing to do with Halloween:

"...The veil
Between the worlds of Soul and Sense
Seemed in the solemn moonlight, pale
And softly bright, to grow less dense;
And dimly shone to mortal view
Of life mysterious glimpses through."

Serrano's veil is between the Real and the Ideal, not the Living and the Undead. Presumably the King James phrase inspired Serrano's thought.

In 1885, Isabella Fyvie Mayo's "Mystery of Alan Grale" waxed a little spookier, though she's still talking about the World vs. Christian Eternity:

"George Vivian had passed away in those hours between night and morning, when it seems as if the veil between the worlds is lifted, so that spirits may slip to and fro."

The presumably influential "Book of Pagan Rituals," by Herman Slater (1978), may be the first to connect the idea with "Samhain":

"Consider that in ancient times this night marked the end of the year, and that on this evening the veil between the worlds was thin."

Why that would be, Slater doesn't say.

It may be no accident that the association of Halloween and "the veil" seems to have taken off with the surge of Wicca in the 1980s.