@fresco,
Gender dress codes.
Separate gender worship.
I can contradict almost all of your points, but will stick with these two.
Not all religions tell us to wear gender dress codes. The gender dress code probably is more a pratical/social thing than a religious. Men hunted, did horseback riding and working in the fields - pants are better for that.
Women needed cloth in a shape which they could wear when pregnant as well as not pregnant. Then fashions came - a social thing.
Inuits wear the same type of cloth. Many natives too in reality more or less none. Scotsmen wear kilts.
Separate gender worship.
The very first Christians stopped that and mixed men and women. They wanted the women to be part of a congregation and not just someone with no voice.
Then the women simply talked so much that a seperation was better.
With Reformation came pews into the churches and again separation of men and women. Not only of religious reasons but also social reasons to protect women from men trying to be too "close".
In Lutheran churches women sat to the left and men to the right. Old icoons show Mary on the left side of the cross and John the Baptist on the right.
The left side was called Mary´s side and the right side John´s side.