I'm not an expert on Medieval Catholic thought. But I know a fair amount about Socrates, and I think the idea that Socrates was gay is itself a modern projection. It's not necessarily wrong. He might have been gay. And it's certainly true that ancient Athenian sexual mores were very different from medieval Catholic ones. But there's more than enough evidence in the dialogues to conclude that Socrates was entirely compliant with those Catholic mores.

We'll start with his wife, Xanthippe, because that's the only documented relationship that we can be pretty sure Socrates had. Xanthippe appears in several sources, such as Plato's Phaedo and in Xenophon, as do the several children the two had. (Some sources suggest they had a bad relationship; I won't get into this because I don't have enough information.) Obviously gay men have been known to have wives and children, given sufficient social pressure. So this doesn't rule out Socrates being gay. But it does incline against it, given Socrates' substantial tendency to ignore social pressure.

Next up is the Athenian lover-beloved relationship. It's a little unclear how common this was outside aristocratic circles, but in aristocratic circles the Athenians socialized their young men by assigning them to older male lovers.

"It was assumed among Athenians that mature men would find youths sexually attractive, and such relationships were conventionally viewed as beneficial to both parties by family and friends alike. A degree of hypocrisy (or denial), however, was implied by the arrangement: “officially” it did not involve sexual relations between the lovers and, if it did, then the beloved was not supposed to derive pleasure from the act—but ancient evidence (comedies, vase paintings, et al.) shows that both restrictions were often violated" (Socrates, Stanford Encyclopedia of Philosophy).

Our sources did seem to think that Socrates found young men attractive. Plato, Charmides, Protagoras; Xenophon, Symposium. But Plato also includes a very odd passage regarding Socrates' relationship with the handsome and charming Alcibiades. It's quite long, so I'll include an abbreviated version in a follow-up.