Hardly any, since the Good Friday Agreement - now threatened by a disorderly Brexit.
But what is relevant to a person's decision to emigrate several generations ago, is the conditions at that time. Before Irish independence the Protestants formed a sort of ruling class in Ireland, their ancestors having come in with or after Cromwell to keep the indigenous population subjugated. That was the cause of the resentment and the drive for independence. The persistence of this ruing class mentality was what led to the Troubles in N Ireland. The police were all Protestant, you could only get a job at Harland and Wolff if you were Protestant, etc etc.
So someone in the past emigrating because they were Protestant is, on the face of it, something requiring explanation.