Those who consider themselves "Irish" or "Republicans" would be found celebrating St. Patricks day. Those who consider themselves "British" or "Loyalist" would be found celebrating the Battle of the Boyne. The Orange Order would be the most adamant of the Loyalist side.
I have a friend of the family who is a 100 year old protestant lady from Belfast and if you were to tell her that she wasn't Irish because she was a loyalist she would have your head. And to say that Irish protestants aren't Irish and therefore should not celebrate St. Patrick's Day is not quite the idea. Although Protestant Extremists might dismiss St. Patty's Day but for the same reasons that Catholic Extremists would claim it for themselves. And for the Republicans to claim St. Patrick's Day for themselves is in a way, kind of an oxymoron. For Republican Extremists claim close ties to their Celtic Heritage, when it was Patrick himself that was the great purger of everything Celt - especially their religion but also many of their customs.

In some places to wear orange on St. Patricks day would indeed be an affront something on the order of wearing Nazi paraphenalia outside a Jewish synagoge or a Ku Klux Klan robe at a NAACP rally.
Just wearing some orange with your green...nah. Wearing a suit, orange scarf and a black derby, yes.
And yes, if you were to go to the wrong neighbourhood wearing an orange unitard waving around the Union Jack.

Cheers,
T.R. Matthews