Your point is contradictory: the taboo isn’t inherently misogynistic but then you seek to point out other alternative past that is no more redeeming. A matriarchy is not necessarily a less sexist origin story. We’ve seen female leaders who are just as sexist as their male counterparts (i.e. Thatcher).
Whatever its origins there are examples of it’s use being deeply misogynistic for thousands of years, enough to taint the taboo with a long patriarchal history. It’s used systemically as reasons for proving female inferiority, and has been used by both men and women. That misogyny has impact throughout the world which this piece shows. A different origin does not lessen the impact that these taboos have on women around the world today.
Yes, there are multiple ways patriarchy has worked to curb women in religion. This piece was never about all ways women are oppressed in religion. That can and has been multiple books for each religion.
My title explicitly points out that this piece merely focuses on menstrual taboos and how they have been an important aspect of religious patriarchy with real world impacts today. It is a lynch pin in many religions for why women are fundamentally impure and other.
That distinction vs hygiene matters because impure is a different connotation, one which Buddhism and Sikhism show can be rectified by focusing on health without sacrificing religious and divine access.
Also your source is a book I can’t even access online so I have no way to know what the author actually did or didn’t say.