Did a bit of a survey with 1901 Irish census.
2434 people named Rafferty (did not look into spelling variations) and of those 2343 were Catholic.
Only 60 were Church of Ireland (23 in Antrim (many born Belfast), 25 in Armagh (23 born in Armagh), 1 in Clare, 2 in Cork (both born Galway), 7 in Dublin (6 born Dublin), 1 in Kilkenny (born Sligo) and 1 in Londonderry (born Armagh))
Also one Church of England (a married woman born Tipperary), 10 Presbyterians. 1 Methodist (born Armagh) and 14 'other' (8 Catholics, 5 basically Church of Ireland, 1 Presbyterian)
Now, onto the records. Many Church of Ireland registers were destroyed after being sent to Dublin for safekeeping to if Mary was baptised COI in Ireland there many not be a surviving record.
Did Mary have any siblings? (especially younger ones born in England) as this might be a way to find mother's maiden name.