As a frequent traveller to ireland by sea and air, I know that checks can and do occur.For travel by air valid photo ID is required but if not a UK or Irish national only a passport will suffice.
If travelling by car your registration is known and logged before you board, and checks do occur. I have been checked both sides and asked for ID. In fact at Fishguard my passport was taken away briefly and on its return I was asked if I minded being contacted at a later date.
(They had obviously looked at some of the visas I had from "dodgy" places one of which frequently hit the headlines at that time.
Once again the rats fire from the hip with no real knowledge.