Please don't. The biggest issue with LGBT integration is the constant singling out. Sexuality is not a character trait. Sexuality, especially in video games, has little to no actual meaning to the story. So even mentioning it comes off as attention grabbing rather than being progressive. If you want to have LGBT characters in games, great. Advertising it as if it's a big deal is simply exploitation.
I was always under the impression that the greatest goal for LGBT people is to be accepted as equals in the community. How are we gonna do this if you are constantly singling them out as if they're special? News flash, having a sexual orientation or gender does not make you special. It makes you equal to everyone else. Pointing out certain sexualities is helping no one but desperate attention whores. That includes all people and especially the media. You're doing a disservice to everyone.
Sexuality and gender does not matter and as soon as people get that into their thick skulls we can move on with our lives and actually improve society instead of trying to split it at every opportunity.
I don't agree with the premise that "Sexuality is not a character trait." It doesn't have to be, but it can be a strong part of a fictional character depending on the type of story they're involved in.
Yeah, nobody singles out characters for being straight, but they don't need to. It's evident in the relationships they have throughout their stories. Spiderman has Gwen and Mary Jane, Supes has Lana Lang and Lois Lane, Nathan Drake has Elena and Chloe, Mario has Princess Peach and Pauline (okay, so there's no sex, but he's gotten kissed).
However, when an LGBT character has a storyline that involves their romantic relationships, people get bent out of shape. Look at the claims that Ellie has become part of the SJW agenda simply because we see her making out with another girl. Same thing can be said about Wonder Woman being hinted as being bi-sexual (which would kinda make sense considering she's in an a community populated only by women). The people that sprang to action to say "keep sexuality out of our comics" never made a stink about her Justice League teammates having their own romances...because straight is the norm so it's accepted and doesn't have to be singled out. But let's not pretend it isn't represented in games, comics, TV, etc.
In terms of gaming, more and more action games are taking a cinematic approach. Like Uncharted and TLOU, the stories surrounding the characters are just as important as the gameplay to fans of those games. This has been around for a long time in JRPGs and other more story based games. And we've eaten up the romances involved in those genres. Adding sexuality as part of a character's defining trait, whether it be straight or LGBTQABCWhatever is adding a whole other layer of storytelling that people have been interested in since storytelling has existed in games or any other medium. But somehow when non-hetero representations of that are shown, people want to act like it should not be important and should be hidden.
There's no reason for this aside from people being uncomfortable with the unknown and unfamiliar. Otherwise, we wouldn't have any characters in games that have romantic relationships or show romantic displays of affection.