I have a passing familiarity with some of the stories from Irish myth, at least in their translated form. One thing that has always puzzled me about these tales is the presumption among scholars that the characters represent gods. Yet the stories themselves almost exclusively talk about these characters as though they were heroic mortals.
This is stated explicitly in Wikipedia, rather more succinctly than I can manage but without references:
Texts such as Lebor Gabála Érenn and Cath Maige Tuireadh present them as kings and heroes of the distant past, complete with death-tales. However, there is considerable evidence, both in the texts and from the wider Celtic world, that they were once considered deities.
While we may suspect a few characters, such as Medb or Cú Roí, of once being deities, and Cú Chulainn in particular displays superhuman prowess, the characters are mortal and associated with a specific time and place
Since these stories were being recorded by Christian monks, it is certainly plausible that they changed the representation of the characters into historical people rather than gods so as not to affront their religion. But what actual evidence is there to suggest these characters were once iron age deities?