General History/Gender In The Old Celtic Religion
In the old celtic religion that was prominent in Ireland, Scotland, England, and Wales during the 4-6 centuries, women had a vital leadership role. Did men have fewer rights or was there gender equality?
I assume you are referring to pre-Christian paganism although your window of 4th - 6th centuries CE seems a little late, especially for England and Wales. 'The Old Celtic Religion' goes back long before the fourth century although the farther back one goes, the less we know due to lack of sources.
If, as you say, women had a vital leadership role, it was due to some form of gender equality rather than a matriarchal culture. Gender equality back then was different than it is today. Back then, women did not want to be men nor to do masculine activities. Instead, many societies recognized female authority in certain things and male authority in other activities. Often, all human activities were divided into male and female categories. Men did not do female activities just as women did not engage in masculine activities. The god of war, for instance, was always a masculine god and had male priests, but the goddess of the harvest, for instance, might be female and would be served by priestesses. Polytheistic religions had both male and female gods that regulated different aspects of daily life. It was only Christianity, with its insistence on one God, who happened to be male, that really drove women out of the priesthood. Roman culture was also very patriarchal and clashed with Celtic culture for many reasons. Any time the Romans encountered a culture with powerful women, the Romans would ridicule that culture and stamp out the matriarchal elements.
Hope this helps,