Had Henry VIII had a different marital experience it seems possible that there would not be the top down reformation which happened in otl.
What happens to Ireland. In olt Catholicism and "original Irish people" were the same more or less.
Well would faith be of no special significance?
Might and Irish form of Protestantism or reclaimed Celtic Chrisitianity beome possible/
Would relations be different overall
Well, the concept of a 'Celtic Church' is an invention of 19th century Romantics and has no real basis in fact. The Irish Church did have some unique attributes and practices on the local level, but this isn't all that surprising; Catholicism of the Middle Ages wasn't as monolithic as many people believe. Furthermore, despite these differences, the Irish certainly viewed themselves as 'Catholic' and not an independent Christian group. So I don't think any revival of that is going to happen.
Now, Irish Protestantism is an interesting notion. I don't know enough of Irish Christianity of that era (a real shame!) to say how successful Protestants were being at that time in gaining Irish converts prior to Henry VIII's conversion. My gut instinct is, that if it does happen, it would likely be Presbyterianism imported from Scotland.
However, its important to realize that the Irish didn't need religion in order to cause them to rise up and see themselves as distinct from the English. The rebellion on Don Cam O'Sullivan and the Irish Republic set up during the English Civil War show that the urge was still there. Hell, half the revolutionaries during the 1798 Rising were Ulster Protestants. So I don't think a Catholic England would naturally lead to a more peaceful island.