Greek Gods weren't homosexual... They might appriciate the company of the same gender but that had nothing to do with sex... I am greek and I know very well my countries mythology...
if memory serves, it was legal in Greece to have a male lover, but once you were married, you had to stop. in Egypt marrying family members were fine, but most people didn't, except the pharaohs, they saw it as a way to grow closer to the gods and stay pure. since the Gods had a lot of brother sister marriages. not trying to insult anyone, just pointing that out.
i don't think there is a 'god of homosexuality' but if you poke around, you'll find one or two who are at least bisexual. especially Greece, possibly Rome, haven't read up on them in a while.
back in roman/ Greek times it was the norm for people to be bisexual. not like today they were ok with men sleeping with men and women and women so all of the god may have been and we only hear stories of their children and they may have not felt the need for one to be for homosexuality because it was so normal and not supernatural.
Adonis was homosexual. He was borned by incest when his mother fall in love with her own father and tricking him to have sex with her, then she got pregnant and gave birth to Adonis. When her father found out that he had sex with her daughter, he tried to kill her. Adonis's mother give Persephone her son.
As Adonis grew older the goddess Aprodites fall in love with him. When Aprodite fall in love with Adonis, Persephone also grew a strong attraction to Adonis. But Adonis amd Apollo were in love. Artemis killed Adonis who was Apollo's lover as revenge because Apollo had also killed her lover Orion. After Adonis's death, Apollo in grief declared Adonis as the god of male beauty and desire.
Zeus had a male lover. So did Apollo. A lot of the gods were bisexual/homosexual because the people of ancient Greece were. It was very much an okay thing in that era and humans see the gods as they are, which gives them (the Greek gods especially) human traits. Some examples are Apollo and Hyacinth, Hyacinth and Thamyris, Hermes and Krokus,and Zeus and Ganymede to name a few.
