For some reason the spiel of 'India has a rich tradition of deep respect for women' always gets my hackles up. I, and most of the Indian women I know, have never really felt respected, safe nor viewed as fully human by our fathers, brothers and husbands or men in general.
But it's true, even if deeply obscured and buried under a mountain of misogynistic crap, so as to be practically invisible on a day to day basis. I know, because I've experienced, it but I think the average Indian woman won't ever, unfortunately.
I don't know about the Laws of Manu, but Vedic tradition teaches that there is absolutely no difference, on the consciousness level and in value, between man and woman. None whatsoever: we have the same consciousness and all apparent differences are merely a collection of man-made "attributes", ie mental stereotypes of false identity and roles, which we cling to, thinking they are "me".
Unlike Christian creationist mythology, that sees Eve as being made from a rib of Adam, Hindu mythology says that God, or original spirit, split into two, resulting in duality and life on earth; but that that original, non-dual spirit is still alive in all of us, the source of all happiness, strength and love; and it's that we seek to return to. (in a very simplistic nutshell!)
A lot of the problems that result in trans-identity could be better resolved through an understanding of Vedic philosophy/psychology, which seeks to answer the basic question of Who am I? What do I really seek?-- which is at the core of the confusion.
Children, and adults, who are taught to meditate ie turn within to find quietude and strength develop an inner stability which would help them/us safely navigate the turbulent and dangerous waters of modern society . This according to research at top universities, including Harvard.