Celtic society may have been matriarchal.
There is a useful document on the internet about women in Celtic society.
I am unsure about the claim in the document that Celtic society was patriarchal, as increasingly as I research my Celtic roots, I see a different reality.
The document takes as its sources the writings of Roman, Greek and Christian writers, all who lived in a patriarchal world view, where man ruled, and woman was his property. Such writers would underplay, ignore, or falsify a worldview that was counter to their own, even demonise it, as the Church often did with women.
As I research the Basques I note they are matriarchal, to such an extent I am unclear how men fit into it. In the mythology the female Basque archetype Mari, is supreme, and she is served by a religious group that appeared to be all female. Until recent times the Basque female was considered either equal to or superior to the male in decision making, especially on the home and children. The Spanish Inquisition tried to exterminate the favourable Basque bias towards women. Basque and Maltese water spirits seem biased towards taking the lives of women and children, rather than men, indicating how important women were held to those peoples.
It is astonishing that no Celtic stories have emerged about a significant figure like Boudica in Britain, but it required a Roman writer to reveal her existence.
Tantalising glimpses emerge from many writings of women being held in a superior light than the writer is telling. The Mabinogion tells of a giant woman with a smaller husband, indicating a superiority of the female in a certain manner.
The Dobunni, a Celtic tribe of South Britain, was strongly in favour of goddess worship.