Basically, thinking about a scenario where the Church of England still breaks away from Rome under Henry VIII, and Ireland stays under English hegemony, but for some reason the Church is much less successful in rooting out Catholicism in Ireland, like how the Poles generally stayed Catholic under Prussian rule.
Obviously a 100% Catholic Ireland is not plausible - given the huge advantages of converting, some people surely would, plus there'd probably be more of an influx of English people to cement their control over the island. But let's imagine Ireland ends up with a Protestant elite ruling over a still largely Catholic peasantry. How would things play out from there?