All I know is when my father was buried in Tipperary a few years back, as an old IRA man from the Civil War days he had a tricolour on his coffin, and it was laid aside when it came to being taken into church.
No priest or antyone making a fuss about it, just the normal way of doing things, and what he'd have wanted - national flags don't belong inside churches. I wouldn't expect to see one at a funeral Mass in a Catholic Church in England either.
If they made a special arrangement for the Mountjoy men, no doubt there were special reasons.
Anyway my father had the military honurs - a firing party out from the local barracks to fire volleys over the grave. (And a cousin said they had to do that - one way and another there'd have been a firing party.)