Those that I fight I do not hate Those that I guard I do not love; (3-4)
The speaker is a strange kind of soldier, one that doesn't seem too patriotic. He doesn't "love" the people he guards—i.e., the British citizens back home. He feels Irish, not British.
My country is Kiltartan Cross,My countrymen Kiltartan's poor, (5-6)
The speaker is patriotic all right, but only when it comes to a really small slice of Ireland: Kiltartan Cross. The people he really cares about, and the ones he really wants to "guard" are the poor back home, not all those nameless people in England and elsewhere that he's never met.
Nor law, nor duty bade me fight, Nor public man, nor cheering crowds (9-10)
Public officials and cheering crowds are usually able to stir up some patriotism. That doesn't seem to be the case here. They don't make a dent in our speaker, who does things for his own reason. He may not even be that patriotic of a dude, as is hinted in the lines right after these.