I think we need a new word. I'm no English major - but "their" seems tied to "they" in my head, and feels plural. It might prove just as confusing as calling her "him" in the past. I dunno.
There's been a few attempts. I see the occasional "Zie/Zir" or "Xe/Xim", both with a "zed" sound at the beginning. But I think you need to rethink how you use "They" every day. Say you are talking to a co-worker, or a colleague, and they are talking about a problem with their boss. you might say, "Why not talk to your HR rep and see what they say about it." (or you might not, depending on your opinion of HR. We all subconsciously use singular they every day of our life, all the time.
I actually wouldn't say that. If I knew the gender of the person I would say it. If I didn't I would absolutely say "he/she". We may... but I honestly try not to. I'm not super sure about my grammar, but I still try to speak clearly and mixed pronouns bug me. But who knows? Our language is evolving - and that may be the next evolution. And why not - we've got to be able to figure out a way to have these discussions. As lines of gender continue to blur in society, so will our rules of grammar that are based on gender. I wonder how other, more gender specific languages will adapt? Spanish ends words with "A" or "O" depending on the object. German is full of verb conjugations based on he or she. Exciting times!"Why not talk to your HR rep and see what they say about it."
We all subconsciously use singular they every day of our life, all the time.
I know in some nordic languages they have implemented the "Hen" pronoun, which is the Neutral. Herr being man, Het being woman, Hen being gender neutral. Perhaps other countries will do the same, or perhaps gender neutral people in those countries will be referred to with the plural pronouns, such as "Ils" in French.