There is a push in certain corners of queer fiction writing to shift all pronoun usage to eschew the traditional ‘he’ and ‘she’ and instead use only gender-neutral forms like ‘zie’ and ‘hir’, as though pronoun usage weren’t already confusing enough — particularly when writing same-sex pairings. Our view on this is pretty simple: gender neutral pronouns have their place, but fiction isn’t it.
Gender-neutral pronouns are very well suited for situations in which the gender of a person is not known or as a way to encompass gender without resorting to the clunky ‘he or she’ structure or the controversial (well, among linguists) ‘singular they’. Their purpose is to avoid the current convention of using masculine pronouns as a default, as in ‘I don’t know who the speaker is, but I know he’ll be great’ and ‘Any student who forgets his homework will get detention’. In both cases, the person being referred to could be male or female — or even identify otherwise — but because English requires number agreement, a singular noun must take a singular pronoun, and unlike some languages, we don’t have a gender-neutral form. (‘It’ is not gender-neutral, it’s agendered.)
But in fiction, there is no need to cover over gender ambiguity because we should know what gender the characters are. Even among trans* individuals, the majority prefer to be referred to using either masculine or feminine pronouns. Relegating them to gender-neutral usages is actually a form of erasure in that sense because it denies them the right to identify themselves the way they are most comfortable. So, in general, stick to the traditionally gendered third person pronouns in your stories, chosen based on the preferred identification of the character in question. It’s less confusing, and makes for a convenient, universally understood shorthand to pick out your characters.
Now, that said, there are exceptions. If you are writing a character who identifies as androgynous, genderqueer, or who (as a character trait) simply rejects the concept of binary gender, then it would of course be appropriate for them to insist to be referred to using gender-neutral pronouns, and for you as the author to use them in narrative as well. However, I would strongly caution any author to do this for story purposes only, not as a way to inject a lecture on gender theory into your work. Readers don’t like to be preached at by their fiction.
Ultimately, as with any writer’s tool, gender-neutral pronouns should only be employed when the demands of the story require them. In the majority of cases, though, injecting them into stories without cause only distracts from the narrative and can hinder enjoyment of the work as a whole.
If anyone has any questions or comments–or would like to open up discussion on what was said here–we more than welcome it. We just ask for people to behave as adults and to be respectful of everyone else. 
Are people (linguists, etc.) still getting upset about the singular use of “they”? I find it to be the most natural and most convenient option in those situations where the subject is unspecified/unknown (i.e. “Who forget their keys?”) and the least offensive in situations where you don’t know which pronouns a person might prefer, and aren’t in a position to ask. Singular use of they is already familiar to most native speakers and sounds natural to most ears in a way that “he or she” never has.
Pssh! Prescriptivists.
Samuel R. Delany did some fascinating stuff with invented gendered pronouns in The Einstein Intersection. But I agree, if you’re not writing highly experimental science fiction, it’s best to keep it simple.
I’ve never run across a story which used gender-neutral pronouns, but I believe it was Heidi Cullinan’s Etsey series that had a third pronoun set. I don’t recall it being gender-related, though; it was a group that preferred to refer to its members by separate pronouns, IIRC. It took me a few minutes to figure out that’s what it was, and I think Heidi did explain it in the story after a bit, but it was confusing at first. I can only imagine trying to use it merely for the SAKE of using it, and how confusing that would be.
Adara — I know one of our authors is currently working on a novella that includes a third gender which uses a third pronoun set. This, if it’s explained clearly in narrative, to me is fine. I’m just a big believer in only including what is pertinent to the story. Throwing in a gender neutral pronoun just to do it isn’t what I’d advise. Doing it because you have a genderqueer character who simply doesn’t fit the ‘he/she’ dynamic? Awesome, do it, and own like nobody’s business.
Without quite knowing what the background of this is, I suspect it originates from the queer discourse corner of, “You can’t know a person’s gender identity prior to asking … i.e. a character in a story who acts responsibly will refer to everyone he/she/zie meets prior to knowing the person’s preferred set of pronouns and identity as zie because that is the ultimately respectful way to engage, no matter how stereotypically female or male a person behaves.” or in fact the somewhat stronger of referring to everyone as zie because it erases gender-boundaries and preset expectations and assumptions.
If that’s the case, I’m somewhat in two minds about it to be honest. I can see why you’d argue for that to be unnecessary, so to speak, and extra baggage but I’m not a fan of dismissing any ongoing discourse as being too complicated or too complex to have a place in fiction. It might not have a place in romance genre fiction but I do think that, since that is the discourse that is happening right now in parts of the community – whether you’re choosing to be a part of it or not (and I’m not), it certainly is a mindset or belief system and, as far as I know, a set of rules that some people live by so I think that yes, it does have a place in fiction if that’s the place you’re writing from. I’d hate to tell a queer-identifying person who, rightly, says that gender identity and perceived gender certainly don’t have to mix (whether in a pre-transitioning state or by choice) or in fact, if that’s the case, that gender is a social construct only without any biological basis, that their way of viewing the world is simply too complicated for fiction and that it has no place there.
Would I regularly enjoy reading books that come from this background? Probably not, but given those queer fiction / gender discourse writers don’t do this for a fad or because it’s edgy or whatnot, but because it expresses their view of the world, I believe that anyone holding that view should feel free to put that into words and write stories about it and write stories using the framework they engage in in their everyday life. Ultimately that’s what we all do to some extent, talk a little about the world as we perceive it, experience it and live it.
I certainly wouldn’t encourage anyone who doesn’t deal in queer discourse to pick this up as something to spice up their books, but I wouldn’t want to dismiss a subset of people and the way they frame their interactions with others as something that doesn’t deserve or shouldn’t be fictionalized. Fiction has always been a way of causing discussion and opening up a discourse or idea for a wider world, so I don’t see why this is any different.
As I said, if you use gender-neutral pronouns unreflected in the manner you describe, without wanting to achieve anything, then yeah, don’t do it. But if there’s an intent there, no matter how uncomfortable it is for readers, or how confusing, then by all means, use them if it expresses what you want to say about the world.
I wasn’t trying to suggest that there was never a reason to use gender-neutral pronouns (GNPs) in fiction. Only that, like you said, if the story isn’t trying to deal with queer issues, then it’s probably unnecessary and clunky to try and shoehorn GNPs into the work. But there have been those who have suggested that any use of non-GNPs is somehow offensive and only reinforces gender norms and stereotypes, and therefore all fiction should only use GNPs. And I disagree with that assessment.