The majority of liberal academia claim the Greeks were very accepting and approved of homosexuality. Meanwhile a smaller group seems to be fighting against the notion that homosexuality was so overtly practiced and accepted.
One front of this divide seems to be the character of Patroclus in 'The Illiad' A minor character outside of his relationship with Achilles. But at some point more modern scholars have begun to portray them as lovers. I remember mainstream YouTube reviewers criticizing "Troy" for making them cousins as opposed to lovers. There's nothing in his original myths or the Illiad poem that states he's gay. He was raised with Achilles in Achilles' dad's court. There is reference to them being closer than brothers but that doesn't necessarily mean gay.
Do you see Patroclus and by extension Achilles as gay?
'Gay' is an anachronism when talking about ancient Greece. Close to no one was 'gay' and those who were, were relentlessly mocked. Insofar as there were homosexual relations, it was bisexual pederasty - men were married to women but also pursued 'beardless boys' (yes, I know it's revolting). Mostly an aristocratic phenomenon, because then as now and at every time, the morals of the rich were quite bad.
In Homer, Achilles and Patroklos were just very good friends. Later on, some portrayed them as lovers, perhaps to justify their own actions. A lot of ancient tales postdate Homer or are different, for example the story of Meleagar, Oidopous and even 'the Judgment of Paris'.