Was there any sort of synchronous "Celtic tradition" similar to what was shared by Anglo-Saxons, continental Germanic peoples, and the Norse?
There's not a lot of information of pre-Christian religion in Ireland. There were draoi (druids) and fili (poets/seers) in Ireland, and they seem to have been the priestly castes.
It seems that the pagan religions died out quite quickly in Ireland, without much of a fight. However, the only real word we have on that is from Christian scholars.
Much pre-Christian religion in Ireland seems to be based on the changing of seasons, which was crucial to agriculture. The sun was an important component, as evidenced by the positioning of stone circles and dolmens.
With the mobility between northwest Gaul, Britain and Ireland, there would have been some similarities in religion, but there are scant sources on pre-Christian religion in Ireland.
Colin Renfrew and Barry Cunliffe deal with religion on Atlantic Europe in their books. I would be interested in reading other redditors opinions on this.
Sorry I can't be more comprehensive than this!