I happen to have a several friends who are transgender, gender-queer, androgynous, genderless, or ambigenderous (I like that word ) in some way or another, and there are lots of people in these communities who prefer the use of gender-neutral pronouns:

he/she == ze
him/her == hir
his/hers == hirs

There are a handful of other pronouns, but I've only seen ze/hir used on the LGBT blogs I read. These pronouns are intended to be used in reference to a specific person, e.g. Pat bought hirself a new umbrella. Most people in the queer community prefer them over singular "they", gender-neutral "he", and the word "it" which should never be used to describe a human ever.

Are there are conventions to accommodate gender-queer people in Esperanto? Would use of "oni" be appropriate or jarring in this context?

I've never heard of LGBT folks in Esperanto using any kind of different pronouns.

However, if you want to find out more about this topic, I suggest asking Sonja Kisa; you could also ask the Ligo de samseksamaj esperantistoj (LSE).

A note, though, although we don't normally use "ĝi" for people in Esperanto, the taboo is much less against using ĝi for people in Esperanto, than for using "it" for people in English. It's not uncommon to use "ĝi" to refer to an animal or a baby - situations where the sex doesn't really matter.

Nothing is stopping gender-queer Esperantists from using a word like "ŝli" (which I have seen used, on rare occasion, instead of "ŝi aŭ li") but I haven't heard about this being done.

Oni means 'anyone' so I wouldn't use it to refer to an individual.

The simplest solution is to use tiu, but I sometimes do use ĝi.

I remember reading about a little group of esperantists in England (Cambridgeshire?)who were using 'ri' instead of li/sxi, except where it was necessary to distinguish gender. That was a long time ago, however. Perhaps some of the EAB people here will remember more about it than I do.

Riismo

This comes from the Wikipedia article Gender-specific pronoun.

In common usage, the Esperanto pronouns ŝi, li, and ĝi correspond to English 'she', 'he', and 'it'. Although its creator Zamenhof recommended using ĝi in cases of unstated gender, this is done infrequently. The gender-inclusive demonstrative pronoun tiu is commonly used instead (a usage that does not occur in English). Reformers have coined gender-inclusive pronouns like ri or ŝli specifically for persons, and 'riism' has in fact made some limited progress.

So Zamenhof intended for 'ĝi' to be the neuter-animate pronoun. I would stick to the rules he put forward and avoid the reformed-Esperanto rules, as the concept of a universal second language requires everybody learn and agree on the same one.

In English, 'it' is the neuter-inanimate pronoun, making it somewhat insulting to use it when referring to a person. This, however, is not the case in Esperanto.

As a side note, in English, 'he' is both the masculine-animate and neuter-animate pronoun.

Tiu seems to be fine. Interestingly 'thon', short for 'that one' was once proposed as a gender-neutral pronoun for English, a hundred-odd years ago.

JulietAwesome:I happen to have a several friends who are transgender, gender-queer, androgynous, genderless, or ambigenderous (I like that word ) in some way or another, and there are lots of people in these communities who prefer the use of gender-neutral pronouns:

he/she == ze
him/her == hir
his/hers == hirs

I've heard of se, ses, sem (since "hir" and "hirs" sound like "her" and "hers" and would thus not be neutral in speech) for he/she, his/her, and him/her. If written "Esperantoly" they'd be pronounced "si, ses, sem."

swfarnsworth:
In English, 'it' is the neuter-inanimate pronoun, making it somewhat insulting to use it when referring to a person. This, however, is not the case in Esperanto.

Honestly, would you want to be referred to as "ĝi?"

As a side note, in English, "he" is both the masculine-animate and neuter-animate pronoun.

That's not the case in everyday language, referring to one person. In those instances, "he" will be interpreted as "male third person singular."

orthohawk:
I've heard of se, ses, sem (since "hir" and "hirs" sound like "her" and "hers" and would thus not be neutral in speech) for he/she, his/her, and him/her. If written "Esperantoly" they'd be pronounced "si, ses, sem."

I'm not a fan of "hir" etc. for that reason. I think my favorite proposed English pronoun set is
ey, eir, em--it's an easy shift from they, their, them.

In Esperanto, I favor "ŝli" over "ri," simply for pronunciation's sake. But then again, "ŝli" is pretty well operating on a binary gender system (seems like "he or she" rather than being gender neutral).

JulietAwesome:I happen to have a several friends who are transgender, gender-queer, androgynous, genderless, or ambigenderous (I like that word ) in some way or another, and there are lots of people in these communities who prefer the use of gender-neutral pronouns:

he/she == ze
him/her == hir
his/hers == hirs

Why not just use "they"? I was under the impression that was the de facto way to refer to the neuter singular. At least in Australia everyone seems to use it that way, and everything I've read in English is the same, so I still can't figure out why these other pronouns are still being made up when there's no need for them.

Heck, I use "they" even for people whose gender I can clearly express as "he" or "her", and I'm surely not the only person who does it that I know, all my family and friends do it every now and then. In writing too I think I've seen "they" over take "he/she" since "he/she" looks too impersonal and ugly, as if you don't care who they are.

Esperanto on the other hand is hard because "ili" makes no sense like that . I think I recall using "tiu" when I've come across that problem, although I have on the odd occasion written "ili" by accident, literally translating what I do in English.

EDIT:
Ah, this might explain why I'm finding this a bit strange -

Wikipedia:In a corpus of spontaneous speech collected in Australia in the 1990s, singular they had become the most frequently used generic pronoun.

Yet...

Wikipedia:Some manuals of style remain neutral on the subject while other style manuals explicitly reject the use of singular they in grammar. According to the Publication Manual of the American Psychological Society, a pronoun must agree in both gender and number with the noun it replaces. The APA manual offers the following example as incorrect usage[clarification needed]:
Neither the highest scorer nor the lowest scorer in the group had any doubt about their competence.[43]
while also specifically taking a stand that generic he is unacceptable (p. 66). The APA recommends using "he or she," recasting the sentence with a plural subject to allow correct use of "they," or simply rewriting the sentence to avoid issues with gender or number.

Wikipedia link
Must be an Australian thing, although I swore it was international. That said, further down it mentions that the NIV Bible uses "they" to reflect modern English, and that's an American translation (Zondervan).