"Except Orangemen do not consider themselves Irish. "

Now that's a dodgy generalisation if there ever was one. If it means all Northern Irish Protestants, it's just not true. If it means all members of those marching organisations with the Bowler Hats, it's not true either.

At one time Unionism was about a minority in Ireland who wanted to keep the whole of Ireland linked to England. More recently it's about one bunch of Irish wanting to stay separate from another bunch of Irish, and making use of the English connection to strengthen their hands.

I don't think anyone has ever suggested that the Confederates didn't consider themselves Americans. (And I believe they hoped at one point of trying to bring in the English to help them.)

Yeah, and I'm sure it's quite possible to find people in Northern Ireland who would say they didn't consider themselves Irish in any sense.