Hmm... I love your question because it has me thinking.
I am familiar with some gender queer stuff, but I have never heard of these pronouns before (or I may have saw them once at most). They sound (phonetically) like "he" and "her" but with a twist. Am I right? If not, could you write out how to pronounce them? (sorry if I sound dumb, but I'd like to get it right if I'm screwing up the pronunciation).
I can't speak for others, but if you corrected me and wanted me to called you ze or hir, I'd be cool with it. I would ask you to be patient with me if I mess up the first couple of times unti I wire my brain for it, but I would do my best to respect your request. And when I screw up, you'd see my face scrunch up and probably say an expletive, so you know I know I messed up.
However, be prepared for questions about it. I would probably say, "Umm, sure. Hey, do you know how those terms came about?" or other things since I'm a generally curious person. I guess, whenever you're in an situation different from "the norm" (handicapped, odd experience, gender queer, minority religion, etc.) you'll have to deal with questions. It's the territory, I suppose.
And maybe my (tentative) faith in humanity makes me think the jackasses you encounter will be the minority. So long as your understanding that the other party is trying to be understanding (be prepared for some odd, non malicious, phrasing), I think you'll be fine.
In reference to your therapist, I don't know the nuances of how she delivered what she said (like body language and tone), but perhaps she said that as a way to see how you would feel and react.
While I understand people should be respectful to what pronouns you wish used, maybe in their head they assign you a different pronoun than you wish to be called. It may not be malicious, and it's just how their brains remember you. And maybe that's what they used to refer to you when discussing others.
At that point, there is no way for you to directly control that situation, and it can cause you stress/pain/anxiety, etc. with no way to relieve it. I guess I'm saying that you can only have a hand in what you see and hear mostly, and worrying about what people do beyond your senses will drive you bonkers. In a way, potentially letting go of some things you have no control over may help.
In terms of employers, they can't discriminate because it's the law (in the vase majority of places). So to hell with them if their jackasses.
Oh, and if you come across a blatant asshole, excuse my French: fuck em.
Dunno... hope I helped in some way or form! Thanks for posting