The Brief: Neopronouns are gender-neutral third person pronouns that are less mainstream than they/them/their pronouns. They include: ze/zir, xe/xir, hir/hirs, and (f)ae/(f)aer.
DEEP DIVE
Neopronouns are third person gender-neutral pronouns that fall outside of the more commonly known pronouns: they/them/theirs, she/her/hers, and he/him/his.
Pronouns To Know
Ae/Aer/Aerself (Fae/Fae/Faerself)
A more extensive list of neopronouns can be found at LGBTA Wikia.
Transgender individuals sometimes use binary or non-binary pronouns, depending on how they identify their gender.