I apologise if this post comes off as lecturing, gender and sexuality are my main focus as a historian so I would just like to correct some misunderstandings in the thread regarding their place in history.
The idea that including LGBT characters in a medieval fantasy setting would be anachronistic is wrong, I am afraid. Unlike today, in the ancient and medieval worlds it was trans and gender-nonconforming individuals who were more visible and respected than gay people. Someone mentioned the hijra of India, other examples include eunuchs in many Mediterranean, Near Eastern and Asian civilisations, sworn virgins in the Balkans, the Vestal Virgins of Rome, and many more. These always existed in a specific religious or political context, such as the eunuch servants of the Byzantine court who were favoured because their inability to create families of their own meant they were seen as wholly loyal to their employers. I'm not trying to say that a trans peasant would have been accepted, but there were specific roles in many cultures which required or were reserved for people outside of the traditional gender binary, even in the most hyper-masculine societies.
Indeed, if you think that including a trans character in a medieval European-based fantasy setting is an anachronism, then presumably you would have to ban female characters from being anything besides wives, mothers, prostitutes and maybe priestesses, because women in history who stepped outside of these specific roles were viewed as violating the boundaries of their gender, unless it was in one of the aforementioned sanctioned roles. Historical conceptions of gender were extremely inflexible for both men and women, look no further than the reaction to Joan of Arc for an example of how a woman who involved herself in war would be viewed and treated, even without taking part in actual combat. And since no one has argued for such restrictions on female characters, I can't see how allowing trans characters would be any more anachronistic.
Non-heterosexual people similarly existed throughout history, and not just in Ancient Greece. For specific European examples, there are many kings who had male "favourites", some of whom came to bad ends but by no means all, as well as overtly romantic letters exchanged between monks. Evidence for female same-sex relationships is rather harder to come by due to the bias of having overwhelmingly male sources. Again, your average peasant probably would not have been able to express their sexuality freely, but for the upper ranks of society, specifically male members things were different. Often, as a long as a man did his duty by marrying and siring children, he could get away with taking lovers of either sex.
First post, hopefully I have made sense.