I am not so sure that Celtic Church is current usage or a good usage. It was a term coined by some nineteenth century church of Ireland scholars. One reason is that the an Iron cultural and linguistic category, a cultural influence not an influx, Q-Celtic in respect of the language, just doesn't seem the right way to class a religious category from 1000 years later. Liturgical uses differed considerably even where Latin had been spoken. Also while polygamy was a feature of Irish society, it was not preferred, the preference being for two spouses of fairly equal standing, as with Late Roman Law, 'lánamnas comthinchuir,' a marriage of joint income. It could be an idea to allow polygamy in some more societies, like on island of Ireland, at the cost of some piety.