Sorry to confuse you but I'm Canadian, not a Saudi. My world is irrelevant. The OP is discussing "paying respects" in Saudi Arabia. I have no idea if the Saudi royal family felt offended by the First Lady's attire or if the people of Saudi Arabia were offended. My point was, as you and others seem to be promoting, if your intent is to offend or to make a political statement, it would be wiser just to stay home. There are other times and better circumstances under which to make your point.
As for your analogy, it isn't one. I'm not aware of any or many in America who are offended by women's attire. If they are, they are free to express that concern in appropriate ways and forums. Doing so while "paying respects" seems more like disrespect to me, but then I've never been one to purposely offend for no reason. If I didn't smoke and I was invited to a person's home where smokers lived, I wouldn't go wearing an anti-smoking t-shirt. I'd either accept the invitation graciously and excuse myself politely if need be, or I'd decline the invitation. You see, it's not for me to tell other people how to live. I have no objection to the First Lady wearing what she likes but if, as seems apparent, she's had no problem with the headscarf in other situations, her not wearing one here seems designed to offend or to make a political statement, both of which are inappropriate under the circumstances.