CupofJoe
Myth Weaver
For them the most popular pronouns would be I,Me, You, Us, and Them. When in need of a word similar to He,She or it I would imagine them just saying One.
I would guess that there would be two version of You too, along the lines of the French language, with a personal/close "tu" and general/distant "vous".
I can also see that given personal names would be highly important and the default way of addressing others. You wouldn't refer to someone by pronoun but by their name. and that would make me think that if you couldn't there would be a word meaning "the name of the person I don't know the name of..." as their equivalent of him or her.
Greg Egan used ve/vis/ver, which I liked. "Ve went to the store to get ver favorite candy." "It's vis problem, not mine."
I think that like Svrtness, this would get to me, but for maybe other reasons. I see ve/vis/ver as lightly disguised he/his/her. That might not be what Greg Egan wanted but I think there is still an implied gender.