I’m at work so I don’t have any books with me but if memory serves the Culdee Church was nothing other than the Celtic Church. It was in communion with Rome but it did have its own rites and liturgy.
One difference was that the primary form of local church government was handled by Abbots, and the position was hereditary. Eventually the obvious problems with a hereditary government took affect and Rome pushed for reform. Now most of that reform happened naturally with Latin rite priests and missionaries displaying more discipline and organization so for many they simply adapted.
Also the Christian Vikings who were in Ireland (Dublin) followed the Latin Rite. This gave a more natural inlet for Latin traditions to take hold.
So in the end while the Culdee rite did have a rich, ancient history. Doctrinally they were in alignment with Rome and always accepted Rome’s leadership. I will agree that it is a shame that a rite that had a strong missionary zeal and who gave us the portable New Testament is now gone. It is historically dishonest to say they were destroyed by Rome or were the first Protestants. The Culdees were thoroughly Catholic.
I believe the idea that they were a “protestant” church was first circulated by the English in order to get the Irish to feel patriotic about the protestant Church of Ireland. The Irish for the most part though didn’t fall for it.