For a historical setting, it's easy to incorporate gay characters since they can be the way they were in history. Likewise, I'd say that in Faerun it is at least defined by the creator. But the question is, what is the right way to introduce gay characters into other fantasy settings? For most settings, they aren't defined as punishing homosexuality the way that Christian Europe did - or having a designated social class like the kliba in India, or the onnagata in Japan - or having open homosexual behavior like ancient Greece and others. Instead, it's left undefined how homosexuality is regarded.
Again, I feel I should note that there's NO period in any culture in ancient history where "homosexuality" was treated the way it is treated in the modern west for the past 30 years or so.
So when you talk about "open homosexual behavior in ancient Greece" it should be noted that it looked nothing like what homosexuality looks like in 2021 USA.
In the ancient Greco-Roman world, homosexuality was not considered abnormal. Many people engaged in it. Most of them wouldn't suggest that was a special identity to them.
Adolescent boys were often put into relationships with adult men; being public about this relationship was seen as shameful and humiliating, but mainly for the boy.
Most adult men who engaged in homosexual activity were also married, and had children. They fulfilled their responsibilities to society, and it was not a huge deal for them to go fuck effeminate men or boys. When someone failed to fulfill their social duties, and it was attributed to their lust for other males, it was shameful (like it was for Maecenas).
In general, there was seen to be no shame in being the guy doing the fucking. But for a guy to be fucked was seen as shameful and weak. This is why when Julius Caesar's enemies said that "Caesar is every woman's man, and every man's woman" it was meant to humiliate him.
This is a recurring theme throughout history in various cultures where homosexuality was tolerated, not universal, but significant enough to jump across big divides space and time and cultures, where it is considered acceptable or even powerful to be the "top" but being the "bottom" is considered shameful and emasculating.
To this day, that sort of attitude still exists in some highly Macho Latin cultures, for example in Colombia and parts of Central America, where a "maricon" is only someone who is a bottom.
So essentially, there were sort of two ways to be "gay" in the pre-christian West, neither of which look anything like how to "be gay" in the 21st century west, and these sexual identities we have today are constructed and not universal.