As far as specific mythological tales, there are a few which I find quite telling in their ability to speak to the equality of the ancient Greeks.
Ganymede was a Trojan youth so handsome that even Zeus was attracted to him. Fearing Ganymede's eventual death, Zeus was overcome by grief and chose to send his eagle to the boy and snatch him away from the land of mortals to the palace on Olympus. There, Ganymede was given immortality and the job of refilling the gods' cups during feasting, a job previously done by Hebe. Furthermore, mythology frequently hints that Zeus took Ganymede as his young lover, much to Hera's disgust.
It was widely understood that the ancient Greeks were agreeable to older men taking on younger male lovers, acting in an all-encomposing way as a mentor to the youth. It is also suggested that often, the legal wives of these older Greek men weren't so welcoming or accepting of their male lover, at least as long as the wife was still able to bear heirs.
Achilles and Patroclus
This widely told and shared story includes numerous elements of just how close the mentor-youth relationship was. Whether always sexual, can be debated, by as for love... well, I'd say that was clear as a bell!
He had poor luck with women, poor luck with men, but equally pursued both. Apollo, unlike the other gods and goddesses, did not seem to prefer one gender over another. In fact, he chased down and seduced any young beautiful youth who crossed his path. And, best of all, no one thought twice about it.
Born a man, came across two mating snakes and struck them with his staff. Turned into a woman. Lived as a woman, marrying a man and bearing at least one child, for seven years. One day stumbled upon the same writhing snakes and struck them again. Turned back into a man. Then, invited to Olympus to help answer an argument between Zeus and Hera. When Zeus asks him, who has lived as both a man and woman and experienced pleasure as both, which gender experiences more pleasure in sex... of course, Tiresias says women. Hera loses the argument and strikes out at Tiresias, ripping his eyes from their sockets. To compensate, Zeus gives him the gift of prophecy and a seven-fold life span.
The ancient Greeks mention very little in their works of literature, beyond this story, the tale of Hermaphroditus (who gets trapped by a nymph Salamis, so unwilling to let him go, despite his protestations, that she melds herself to him, gonads and all), and my next tale about Zeus disguised as Artemis, about transgenders, however considering the three stories told, I'd say they were probably at least acceptable of the idea.
The rest of the stories above seem to involve some form of acceptance or consideration, except this one. In this one, the raped woman, the Lesbian, is declared at fault and punished. The ancient Greeks may have been considerate of other relationships beyond the straight heterosexual, but definitely weren't overly forgiving of female-female sexual encounters.
Interesting, still, yes?