So please enlighten me if my knowledge about its arrival to Ireland is wrong. I would be glad to learn something new and change my mind.
Where do I start?
Christianity arrived in Ireland because a British slave called "Patrick" brought it there. So according to your logic the Irish would still be pagans if not for the British.
This Celtic church was introduced into Britain and was fairly popular until the synod of Whitby where it was decided that England (or at least Northumbria) should be a Catholic state.
Catholicism was brought to Ireland by a Norman invasion through Wales and blessed by the one and only English pope.
Protestantism arrived in Ireland via Henry VIII who had inherited his Irish lands through the Norman kings.
So whilst you are technically right in what you said, you missed out on over a thousand years of religious inter-connectedness and that's without mentioning pagan connections between the Celtic Britons and the Celtic Irish.
And lastly your conclusion about Britain wanting to retain Northern Ireland is simply wrong. The British were not giving independence to Ireland in 1922, they were giving an equivalent to dominion status. The idea was that Ireland would be like Canada and remain within the British sphere whilst governing itself. As a result, they were genuinely annoyed with the Ulster Protestants for messing things up.
And Republican guarantees were a joke. After independence the IRA went around burning down "great houses" and carrying out minor bits of ethnic cleansing. The Protestant population of the Republic of Ireland fell dramatically. The Ulster Protestants weren't going to sit around and let the same thing happen to them and thus civil war was inevitable.