What do we know about Irish religious beliefs and practices? What were Irish spiritual priorities?

There are no contemporary accounts of pre-Christian Irish religion. If any Greeks or Romans traveled to Ireland, they left no written accounts. The Irish themselves adopted writing when they adopted Christianity. What is known of pre-Christian Irish belief and practice is inferred from archaeological evidence, myths and legends recorded by the Christianized Irish themselves, folklore and custom recorded largely in the nineteenth and early twentieth centuries, and by analogy with their ethno-linguistic cousins like the Gauls and Britons. All three types of evidence are attended by serious interpretive difficulties, with the result that there is a fair amount of scholarly controversy and disagreement. I'll talk a little bit about the evidential problems, then the broad outlines of what most scholars would agree on, and then suggest some further reading.

First, the evidence. Archaeological evidence related to religious belief and practice is indirect. One can, for example, find plenty of archaeological evidence that allows a scholar to describe in great detail how a culture buried its dead. Beliefs about the correct way to bury the dead are usually rooted in religious beliefs, but knowing how a culture buries its dead is still a very long way from knowing what the specific religious beliefs were that dictated those choices. All the myths and legends the Irish recorded from their pre-Christian forebears were committed to writing centuries after their conversion, by people deeply knowledgeable about the Bible and well-acquainted with Classical (i.e. Greek and Roman) literature and mythology. These stories were certainly carried transmitted orally for centuries, and we know that oral literature can be preserved in remarkably intact form for generations, but that oral tradition disappeared (or at least changed beyond recognition) sometime after the stories were committed to writing. Scholars therefore have no very good way to determine to what degree the myths as we have them are faithful transcriptions of oral tradition, as opposed to literary creations inspired by Classical myths and fleshed out with local detail. Most of the earliest Irish versions of these stories are not in verse, which is problematic because verse forms act as a kind of built-in error correction to ensure faithful transmission. Scholars in the nineteenth and early twentieth centuries tended to assume that surviving folk practices and customs in their time reflected immemorial tradition. These were assiduously recorded by collectors both amateur and profession and have at times been treated uncritically as direct witnesses to pre-Christian belief and practice. More recent generations of historians who study folk custom, like Ronald Hutton, have demonstrated however that folk custom is and was a living set of practices, not a fossilized remnant of a bygone age. Finally, inference from analogy with their Briton and Gaulish cousins is a problem for two reasons. First, the Irish and these related peoples had already been traveling along separate cultural paths for many centuries before the Greeks and Romans recorded anything about them. Second, the Greeks and Romans were neither all that interested in "barbarian" religious beliefs nor very skilled in recording or interpreting them. Thus attempts to, for instance, interpret a piece of pre-Christian Irish archaeology with reference to something Caesar wrote about the Gauls cannot avoid being pretty tenuous.

All that said, there are some widely accepted generalization based both on broad cultural patterns for the Celtic peoples as a whole, and on specifically Irish evidence of various kinds. It is reasonably clear that the Irish were polytheistic and worshiped a variety of personified deities not greatly dissimilar to those worshiped by the pre-Christian Greeks, Romans, Norse, etc. Details of this worship are quite difficult to tease out, however. The Irish do not appear to have had anything quite like the Greek or Roman temples, though they did apparently have some enclosures and earthworks used as ritual centers. Certain springs, lakes, mountains, etc. were also places of worship. Animal sacrifice and the ritual breaking and deposition of objects like weapons into pits, wells, or bodies of water are methods of worship that are attested from archaeological evidence, though again it's not easy to interpret the full significance of such practices. It is pretty clear that, like other Celtic peoples, the pre-Christian Irish had a class of priests known as druids. The functions of druids extended beyond the strictly religious domains into diplomacy and law as well. Bards or poets were also regarded as religious figures to some degree and, judging from literary evidence, engaged in divination. The religious calendar seems to have been geared less to the agricultural cycle, as was the case in Greece and Rome, than to the cycle of pastoral livestock husbandry, which was a rather more significant economic activity in Ireland. Special Irish names and a lot of folkloric practices are attached to the dates of February 1/2, May 1, August 1, and November 1. Other folkloric practices and customs cluster around days like St. John's Day on 24 June, which may reflect a previous religious significance to the summer solstice. The recorded myths and legends recount a plethora of character who may or may not have been regarded by the Irish themselves as objects of religious worship. One of the longest sustained mythological/legendary narratives, the Lebor Gabála Érenn (Book of Invasions of Ireland) recounts the settlement of Ireland by a whole series of "invading" peoples, at least some of whom were probably regarded as gods and goddesses at some point. The existence of a kind of alternate reality called the Otherworld, populated with creatures not immediately distinguishable from humans, is a very strong theme in the early Irish literature that also carries through into folklore. In more recent times, Irish folk tradition held that the Otherworld was where fairies (who were not easily distinguished from humans at all) normally live. Scholarly opinion seems to be divided about whether the Otherworld was a realm of gods, or an afterlife, or both.