Another such language, though fictional, is Mando'a. Mando'a is spoken by the Mandalorian faction in Star Wars. As stated by the creator of the language, Karen Traviss, Mando'a is regularly gender-neutral.
Gender nouns are the same for men and women. Gender is implied contextually, if relevant. Where gender clarity is necessary, the adjectives jagyc (male) or dalyc (female) are added.
Karen Traviss on her personal lexicon
The word for parent is
buir, and it is used regardless of whether or not the parent is a birth parent or an adoptive parent. Family is highly regarded in Mandalorian culture, but in a manner that is very much different than the Pirahã in @Yellow Sky's answer. There is very little emphasis on adoption versus birth, and families (known as aliite, aliit singular) are made up of larger organizational units comprised of those related by blood, family friends, and pets. They are also lead by a clan buir who is responsible for leading and representing the clan.
When addressing a parent, "buir" is often used as a suffix, much like Japanese Honorifics. Kal Skirata, the Mandalorian training sergeant responsible for training Omega squad, is called Kal'Buir by the clones he trained. This is because of the relationship they shared on Kamino, but also because he later adopted the members of Omega squad as his children.
To address the specific questions at the end of the post, "buir" can be treated very much like the Japanese honorific Sensei. When addressing a teacher or speaking of them, they can either be addressed as "Sensei", context permitting, or addressed as their name followed by "-Sensei", such as "Akari-Sensei".
Also, it is important to note that this post draws heavily upon Star Wars Legends, but that's a topic for another SE.
I can only post two links, otherwise I'd post more sources for my post, but some reading points are the Mando'a Legends page on Wookiepedia and The Mandalorians: People and Culture by Karen Traviss as printed in Star Wars Insider 86.