Three terms to describe some features of Hawkfolk society. This society is
Patriachal,
Matrilinear and
Avunculocal.
Although like ancient Nordic and Celtic societies (or most modern Fantasy fiction societies) the Hawkfolk look very good when compared to Victorian England, Ancient Greece, or 19th century America, on issues of Women's rights, this is a society where men are dominant. The Hawkfolk are often described as an Amazon society in Meglos and Al-Wazif, but that's a common reaction to societies that are less repressive of women.
Matrilineal means that descent, and in Hawkfolk society inheritance, goes through the female line. In Europe, the "Son of the Father" was the heir. Among the Hawkfolk the "Son of the Mother" is the heir. This leads to a relaxed view of sex in general and homosexuality in particular. In Patrilineal societies, it's vital to know who the child's father is. Thus chastity and sexual fidelity for all women are vital. Since it's normally vastly easier to know which woman is the mother, matrilinear societies don't need to focus on sexual control.
Avunculocal societies are a type of patriarchal matrilinear society where a man's heirs are his sister's children. The former King was Alerion's maternal uncle. The most capable children of Alerion's sisters will be candidates to be his heir. The family home and/or lands passes from the uncle to his nephew (occasionally his niece).
The society of the Hawkfolk isn't strange to anthropologists, but Yttarria's humans will find them strange and warped.