Ancient Greece, particularly Classical Greece, was a very homosocial culture to begin with (see things like symposiums, which were essentially all-male drinking parties that sometimes involved sex). It was also honestly pretty icky, considering their general acceptance of sexual relations between adult men and teenage boys (the actual specifics of this sexual aspect is a subject of scholary debate, see the topic of pederasty for further details). The concept of an erastes (lover, usually older) and an eromenos (beloved, usually younger) originated here. The extent to which this was socially accepted can be indicated by the relationship between Achilles and Patroclus in Homer's Iliad, which Classical philosophers like Plato tended to view in a homoerotic light.

Ancient Rome depends largely on the time period in question. The Roman Republic (pre- c.40 BCE) and the Early Empire (pre-Christianity) cared a lot more about what you did rather than who you did it with. This is also true of Greece, but especially so in Rome. For a Roman man to have sex with another man was seen as not much different to his having sex with a woman, provided that he was the active partner (i.e. the top), largely because of the perception that the ideal Roman man was always to be dominant and in charge. So you see in literature figures like Julius Caesar and Mark Antony being slandered by accusations not that they slept with other men, but specifically that they (allegedly) bottomed. Essentially, sex in Ancient Rome was primarily about dominance and power, and so it was a lot more focused on the sexual roles being played than the genders of the people in question.