Does religious tradition hold that the 12 tribes of Israel share a common matrilineal ancestor, and if so who was she?
The tradition is that each tribe was descended from one of the 12 sons of Jacob, who fathered six by his wife Leah and two each by his wife Rachel, who was Leah's sister, and the handmaidens Bilhah and Zilpah.
Another question asks for the name of Leah and Rachel's mother. It seems that the Book of Jasher (chapter 28, verse 28) names their mother as Adinah, whereas the sefer Tiferes Shlomo al HaTorah in Parshas Vayetze describes the two women as having different mothers, whose names I do not know.
As for Bilhah and Zilpah, they too are described as either sharing a mother or having two different mothers. According to the Testament of Naftali, their father was Rotheus and their mother was Euna. According to sources including the Midrash Raba they were fathered by Laban, who was also father to Leah and Rachel, by two different mothers. If that is so then we get all 12 tribes descended from Laban as well as from Jacob, but this does not tell us of a shared matrilineal ancestor.