Which cultures have historically considered the manifestation of two or more genders by one individual to be either a divine trait (being a deity) or to be an indication of divine favor or association (being a priest or prophet, etc)?
If we accept mythological and "divine" figures as having "divinity" or being "sacred", here is a short list from the Hindu pantheon, and by no means exhaustive:
Ila: Is both sexes, changing sex seasonally. Married to Budh or Mercury-God (planet Mercury). Goes through many transformations.
In the Ramayana, the Linga Purana and the Mahabharata, Ila grows to become the king of Bahlika. While hunting in a forest, Ila accidentally trespassed Sharavana ("Forest of Reeds"), the sacred grove of the goddess Parvati, the consort of the god Shiva. Upon entering Sharavana, all male beings except for Shiva, including trees and animals, are transformed into females. In the Ramayana, even Shiva had assumed the form of a female to please the goddess. One legend tells that a female yakshini disguised herself as a deer and purposefully led Ila to the grove in order to save her husband from the king. The Linga Purana and the Mahabharata emphasize the sex change of Ila to be a deliberate act of Shiva to start the Lunar Dynasty. The Bhagavata Purana et al. texts tell that Ila's entire entourage as well as his horse also changed their genders.
Ardhanarishvara: Made of Both Shiva and his consort Parvati, usually depicted as split through the middle. Right half is usually male- Shiva. Some say it is the representation of unity/yin-yang/completeness.
Ardhanarishvara represents the synthesis of masculine and feminine energies of the universe (Purusha and Prakriti) and illustrates how Shakti, the female principle of God, is inseparable from (or the same as, according to some interpretations) Shiva, the male principle of God. The union of these principles is exalted as the root and womb of all creation.
Shikhandi/Amba: Born in one life as Amba, she comes back as ambiguous/female Shikhandi to take revenge on Bhisma.
During the great battle at Kurukshetra, Bhishma is unable to fight Shikhandi, who is fighting as a man, but whom Bhishma knows to be a woman.
According to C. Rajagopalachari's Mahabharata summary, when Shikhandini was still a young woman she discovered the garland of ever-blooming blue lotuses hung on the palace gate. Shikhandini put it around her neck. Actually it was Amba (now Shikhandini) who had hung the garland given to her by Lord Kartikeya. When Drupada saw his daughter wearing the garland, he quaked with fear at the thought of becoming Bhishma's enemy and Shikhandini was banished from the kingdom. She performed austerities in the forest and was transformed into a male named Shikhandi. According to Vyasa Mahabharata Shikhandini exchanged her sex with a Yaksha.
Arjuna: The hero of Mahabharata also changes gender. Urvashi cursed Arjuna when he refused her advances, that he would become a "kliba", or of third gender. Arjuna used this as a disguise during his last year of exile, taking the name Brihannala and living as a woman.
Vishnu: Changes gender and becomes "Mohini" (the enchantress) to trick the demons into giving up "Amrita" the nectar of immortality. Vishnu as Mohini became pregnant from Shiva, and gave birth to Ayyappa.
According to Tamil versions of the Mahabharata, the god Krishna – an incarnation of Vishnu – also took the form of Mohini and married Aravan. This was in order to give Aravan the chance to experience love before his death, as he had volunteered to be sacrificed. Krishna remained in mourning in the Mohini form for some time after Aravan's death. This marriage and death of Aravan are commemorated annually in a rite known as Thali, during which Hijra (Indian "third gender") take on the role of Krishna-Mohini and "marry" Aravan in a mass-wedding, followed by an 18-day festival.
Iravan/Aravan: God of transgender community and the Drapadi cults. Also married Mohini (sex-changed Vishnu).
Yuvanashva: The pregnant King.
Sthunakarna: The yaksha who exchanged sex with Shikhandi.
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