(In France, women "of a certain age" are usually referred to as "Madame", whether or not they are married. Female salutations are used in similar ways in other cultures; i.e., "senora" and "senorita" in Spanish-speaking countries, and "signora" and "signorita" in Italy.)
Having said those things, I believe that a person should have the right not to identify as male or female. Such a person should be allowed to create another gender identity, or not to have a gender identity at all.
Interestingly, some other countries are, in effect, allowing that. Four years ago, an Australian who goes only by the name Norrie was issued papers that say "Sex Not Specified." As I understand, a few other people have received such papers.
Now people in the UK can get drivers' licenses and other official documents on which their names are preceded by "Mx."--which is usually pronounced as "Mux"--instead of "Ms.", "Mrs.", "Miss", "Mr.", "Dr.", "Lord" or "Lady". Royal Mail, the country's major banks, government agencies and some universities are now also acepting this title. It even appears in the drop-down boxes of some online job applications and other forms.
It will be interesting to see whether the title is adopted here in the US. I am old enough to remember the uproar over "Ms." when it first appeared. Some people actually thought it was the end of civilization when the New York Times started using it in their articles in the late 1970's. If Americans start to use "Mx>", how long will it take the Times to allow it onto their hallowed pages?
I also have to wonder how or whether other cultures that don't have an equivalent of "Ms>" will deal with "Mx."