Brían, thanks for that.Máirtín Ó Cadhain compared Joe's singing of that song to a Fra Angelico painting. I've just been reading an article by Angela De Burca on Irish religious songs in The Companion to Irish Traditional Music (ed.Fintan Vallely, Cork University Press, 1999).

She writes about a small corpus of songs which mainly focus on the crucifixion. Some songs were collected by Douglas Hyde, and published by him in 1906 without tunes as Amhráin Diadha Chúige Connacht/The Religious Songs of Connacht.
Angela De Burca continues: "other religious songs...were almost forgotten until the 1960's, when the Catholic church's adoption of liturgies in vernacular languages inspired a revival. Meanwhile the recordings made by Seosamh Ó hÉanaí in the 1970's have ensured that his have become the standard airs for...these songs...Versions collected from oral tradition can be up to and over a hundred lines long, sung slowly, and with a refrain after each line"
She refers to some other recordings in addition to those by Ó hÉanaí; Caoineadh na Maighdine on Gael-Linn sung by Nóirín Ní Riain, with the monks of Glenstal Abbey, and Lights in the Dark on Warner/Detour.
So, yes, there is an Irish tradition of singing religious songs (but not psalms), which has been revived in the modern Catholic Church.