I'm not confusing anything. I've argued on this very board that FGM is not a uniquely Islam thing.
Yes, culture is a big influence, no arguing that. Religion is one fundamental part of culture. Do you not agree? The cultures where the "least common denominator" we're talking about is missing has the highest equality between the sexes. Is culture unwilling to relinquish control over women, or the religion unwilling to relinquish control over culture? Makes little difference to the outcome, I'd say.
The Hindu portion of our discussion is inextricably linked to geography, and shared history with Islamic neighbors. As far as I know that religion has no differentiation in value between the sexes, and there have been female presidents in India.
As to the lack of female US presidents? Let's not confuse a true patriarchy where different people have different values even in some legal applications, with a republic where sexist attitudes are rapidly disappearing. Hillary lost because she was disliked and not trusted, not because of she's a she.
Edit: I completely overlooked your point of female heads of states in Muslim majority countries. Point to you, and it shows a certain bias on my part.