No it was invaded because Normans were setting themselves up as independent of the English state and ruler of said state could not tolerate a rival center of power and legitimacy.
Ireland wasn't invaded because it was Catholic. It was invaded because it is a staging ground for easy invasion to England.
Remember that England invaded Ireland a number of times:-
1) the Plantagenet invasion, which Zen9 more or less correctly categorises, there was a bit of concern by the Church about religious unorthodoxy and possible heresy and landless younger sons pushing for an opportunity to establish themselves to add to the mix as well;
2) The Tudor invasion, mainly prompted by the role of the Fitzgerald dynasty in backing Perkin Warbeck and Lambert Simnel's rebellions, I suppose also meeting Zen9's definition;
3) Cromwell's invasion, mainly prompted by Ireland's support for the Royalist cause in the Civil Wars;
4 King William III's invasion due to Ireland's continuing support for James II.
So Zen9 is correct in the main in terms of motivation for invasion.
OTOH Socrates is correct in that this was the main strategic driver for a continuing British military presence in Ireland .
And they're further away. And they have much less history of English involvement than Ireland did.
As I recall from my university days, the Catholic Mary was much keener on Irish plantations and forcing the Irish to conform to English law and custom than the Protestant Elizabeth was. A Catholic England might not have been any less repressive to the Irish than Spain and France were to the Basques or than France has been to the Bretons. Indeed, without the religious bar, more of Irish culture may have survived OTL than would have TTL.