Ireland was at war long before republican rebels fanned the flames
Apart from the fact that sectarianism has been a feature of Irish socio-political life since the Tudors engaged in a Protestant plantation of Ireland, the first serious instance of violent sectarian division in 20th century Ireland was of course the Ulster unionist revolt of 1912.
This came in response to Home Rule, not to 1916. Unionists wanted to ensure Protestant settler hegemony and privilege, particularly in the North. It didn’t amount to bloodshed only because the British government backed down and its army mutinied.