When living in London last year I had a huge debate over this issue (same time of course). He (also Irish) refused to observe the minutes silence at work and instead went to the toilet. I thought he was being a hypocritical x y and z, he was working and living in the UK after all.
My argument was that there were many Irish who fought for Britain during the 1st world war especially, there's a memorial in our town and that he was just being your average moronic 'hate the queen' and all things British, Irishman. (A 19 year old caused havoc recently because he wouldn't fold a pair of union jack boxers in a shop in Dublin - yes there are people in Ireland who are that narrow minded. I say that because he has most likely not been impacted in anyway by historical events and probably has received very little education on the history)
Having read McClean's letter I have to say I agree with his decision, now that I know it's celebration does not include Irish soldiers who fought for the British in ww1 and instead celebrates brave men of other campaigns.
On the matter of Celtic, if you understand the history of the club and really understand it and what it represents, who its founders were, who its supporters were and are then you would surely understand why the club could NOT wear the poppy.