Celtic Distinctives
The Eastern Churches grew up within the Byzantine Empire and adopted forms that mirrored the way society at large was structured.
Unity of Creation   Natural Revelation   Love of Learning

Monasticism     Anamchairde     Holiness     Peregrination
The Roman Catholic Church grew up within the Roman Empire and largely replaced it as the governing force in the West following the "barbarian" invasions. Its forms reflect that heritage, and all the Protestant offshoots from the Roman Church are similar in their hierarchial arrangement.
While the British Church of the early centuries maintained a hierarchial, episcopal form of governance, the Irish churches that sprang up with such vigor after Patrick's death were totally different.
The Celtic societal structure was patterned around families. Each clan had its own territory and governed in its own manner. The Irish churches reflected this in their governance and their resulting independence of thought and practice.