The revised and enlarged edition of _The Course of Irish History_. T.W.
Moody and F.X. Martin, eds. Dublin: The Mercier Press, 1984 would, I
believe, give the non-specialist an overview of religious problems in
Irish history from early times to the present century.
A particularly interesting book is _The Church and the Two Nations in
Medieval Ireland_. J.A. Watt. Cambridge: Cambridge Univ. Press, 1970.
It deals with the struggle for control of the Irish church from the time
of the Norman invasion up to the Statutes of Kilkenny. I think it is
worth reading because it gives a picture of the religious conflict
already brewing when there was still only a single church.