I don't know if that's true. One of the first lessons of effective counterinsurgency is a good understanding of local culture* -- that's different from "respect."
I don't think the point is trivial. The way Muslims barbarians mistreat women is directly related to the way they mistreat each other (and the Western world) in other ways. If we can show them a different way for men and women to get along we're teaching them a lesson about how to act more civilized.
* The relevant Special Operations Imperative says, "Understand the operational environment," and that includes culture. It doesn't really say anything about "respect."
Good point.