If someone doesn't "identify" as a man, or a woman, can they really get all that bent out of shape by someone using either pronoun to address them? 

It should be up to the individual to introduce themselves, and speak up when someone addresses them by a pronoun they don't like. No different than when someone mispronounces your name. Politely correct them. 

What bugs me about all this is that we are basically passing laws against hurting someone's way-too-delicate feelings. It's a result of people not being equipped to stick up for themselves and appealing to some higher power to do it for them.   

This is a result of the anti-bullying campaign from a decade or so ago. People don't learn the basic adult life skill of sticking up for yourself.