Gender recognition depends on the region. Both Zizumbir and the Northern part of the Empire only recognize two genders but accept transitions between them to varying degrees. The people of Razendi's region recognize a third gender typically assumed to be intersex, but they might have a hard time recognizing a trans person as anything other than third gender. The official term is unhalved. The region is influential enough to normalize the use of they/them pronouns within the Empire for those who request it. We'll get into more detail about Zizumbir's specifics later.
By the way, a gentle reminder that Kiri's pronouns are they/them! Unhalved people are referred to by their job title in polite speech, so Jintu would call Kiri "Assistant Kiri" the same way he would call Tashti "Miss Tazilka." This was demonstrated earlier when the little girl (Lilanthi!) referred to Uzha as "Soldier" when her gender was unclear.
Unhalved people are welcome in any single-gender space but specifically in these spaces they are treated as a member of the gender the space is for. They are seen as being both genders rather than neither.
These notes are purely based on my own personal fantasy world and not generalizations of real live people.