Ireland is not part of Britain.
So it shouldn't be considered as the British Isles, IMO.
I don't blame you, given recent history, but I thought the term 'British Isles' for the archipelago pre-dated the Empire by a loooong way. 'Great Britain' itself is a comparatively recent name, barely 200 years old.
In AD70, Pliny the Elder wrote Albion ipsi nomen fuit, cum Britanniae, ie that all the islands of Albion were known as the Britannias. He included what is now Great Britain and Ireland. Ptolemy also included Britain and Ireland as part of the same group.
Anyway, I guess more recent history trumps the older names.
I dunno what the island group should be called, so.
Anglo-Celtic Isles?
And South America and Central America are not part of the United States of America. Should they have to come up with new names?