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There are gay dudes, gay women, bi people, there's married gay couples. Players can marry same gender. Everything. None of it is ever portrayed negatively or for comedic effect. It's just there sometimes. You don't have to go out of your way to find it either, you directly encounter a chunk of it on the main quest line.
This game has absolutely zero concern with lgbt content. Anyone that has played this game will not believe myths about official censorship of lgbt content having directly seen for themselves that it's not.
it's a wandering tale quest so there's no trigger other than talking with the person who starts the quest
if you check your journal for the list of kaifeng's wandering tales, there should be one called "All Creatures Great and Small"