I'm gutted to have missed episode 1 of Banishing Eve, however, my DH summarised it as follows:
Until around the 10th century (I think I've got that date right), if you had asked anyone who built the Christian church, they'd have said: women. Women were instrumental in every aspect of running the church, leading, teaching, etc etc. It was only later on that certain male church leaders decided to clamp down on this and dominate the women in their communities.
There's also information about certain books of the Bible which were either written by women, or which primarily tell the stories of women, which were long ago cut out of the Bible.
This says very clearly to me that it is the 'standard' patriarchy that stems from bigotry within society which has led to the patriarchy which has dominated women within religion.
With this in mind, it seems a relevant question to ask the following: since 21st century life still places women in a lower position to men in many ways, why do women not simply absent themselves from male society and go ahead and create their own society which is devoid of misogyny? This is the same question which is being asked on this thread of women's involvement in religion. Certainly there are pockets around the world where women do this (dittany, I believe you once posted on a thread about a group of Kenyan women who created a women's village because they were so fed up with the maltreatment they were being subjected to - it was you, wasn't it?). So if the answer to the problem of patriarchy within religion is for women to remove themselves, surely the answer should be the same for the problem of patriarchy within society as a whole?