No.
If those things are added for the sake of adding them, they are distracting. It is an artificial thing. Every stone is hand crafted and put there with a purpose. If there are things that only scream: look, how inclusive the setup is! The developer scratched all check marks for diversity and representation... Nah. That's screaming to me, that they care more about self represenstation and virtue signalling than about the story.
So if there is a story purpose or it is part of the main story, ok. Tell the story. Otherwise, it breaks immersion. Makes you wonder why it is there.
While not lgbt, nor a game, I recently watched Red Riding Hood (2011), an adaption of the fairy tale about the wolf and, well, little red riding hood. There was a priest that had an entourage of soldiers. Two of them were Black and one looked Asian. While such a thing might have been historically possible, it distracted. It served no other purpose than to show off the film makers virtue. They could have hand waved it with an introductory line, that the priest would have been a travelled man that collected all sorts of exotic followers and gear. Must have missed that. Oh, and the immersion breaking was, because none of the remote villagers even bat an eye about seeing those soldiers. Most of them never would have left their village. They are not cosmopolitans. All that was missing was a lgbt subplot to round it off - and none of the religous villagers having an issue with that to fully break immersion.
For rpg, if there is no romance in it, why even mention the sexuality of characters. If the game developer does, but does not include romance related plots, that was an informed quality of the character for the sake of mentioning it.