Ah, I see. Yes, that is correct, the island originally had a church semi-independent of Rome, so there is some justification in calling it non-Catholic. One of the big areas of debate in Irish church history is was the church Roman or not, so certainly that view is a valid one.
Full "Roman" Catholicism took over in the period you mention, basically as a consequence of the Norman invasion.
What I was getting at is that the non-"Roman" church which existed in the Old Irish period (so called because all texts from that period are written in Old Irish, a literary standard) had a lot of elements to it that I would imagine (although I could be wrong) you wouldn't consider very Christian and maybe possibly worse than Roman Catholicism.
That is, I'm not sure Celtic Christianity would be any more palatable than Roman Catholicism to modern Protestants.
Of course it's very sad to me that Ireland has lost its Christian character if that's true.
Well in the turn from Roman Catholicism, the two major alternatives have been American style evangelism or deism/atheism, so probably the number of Christians has gone up as far as your concerned!
I should say though that our Christian/Catholic character is mostly a result of the famine. In the 18th century for example virtually nobody attended mass and having heard or read any of the bible was considered noteworthy even for a literate person. To give you an idea our native poetry (in Gaelic) rarely contains any reference to the biblical imagery.