There are more inclusive character generators in World of Warcraft: Dragon flight. The alpha release of the expansion has removed gendered language from the character creator. Instead of the male and female options you often see in these tools, they're now divided into two separate sections. You can now build a gender non- conforming adventurer without any awkwardness.
Code found by Wowhead suggests that you may be able to choose who you want to be called in a future release. The most recent alpha version of the game pulled references to a possible way to choose your character's voice.
The changes may not be as significant as you want. It's not possible to have facial hair and breasts on the same person. If you don't fit into traditional gender representations, World of Warcraft could be more appealing.