Attempting to take another argument's words literally when their intent is obviously quite different is a rather poor way to create a counterpoint. But, I respect your opinion regardless.
Of course there is (generally) no physical contact between the sexes in a public restroom. Duh.
For your words of, "It does no such thing," I point you in the direction of what seems to be a majority of Americans leaning towards the "right" in this country as of January 2015. I'm pretty sure the data has become more extreme in variance with the decline of moderates in both parties. (http://www.gallup.com/poll/180452/liberals-record-trail-conservatives.aspx) These people believe that there is significant harm done to societal structures that may have been in place for decades, if not centuries. This same train of thought is not only shared by ~38% (+ right-leaning moderates) of American society, but for other societies around the world, including the Islamic ones you mention.
At this point, our opinions can be considered "subjective" and can be either confirmed or denied by people with the same or opposing ideological beliefs and philosophies. We have reached the point where there is "no one right answer" to this subject.
We could continue to debate over this but we would not reach any closer to the truth, whether or not this North Carolina law is upheld or struck down in court. It will not resolve public discourse.
One more thing, I see you calling Muslim societies "malignant"... I would *love* to dip into the subject of the "Intolerance of Intolerance" found thriving in the left wing of American politics, but that is a topic for another time... I find your words for their society to be quite... intolerant.
What a great irony, if I may say so for myself!