Not actually sure if we're supposed to be posting our gender and sexuality, but a lot of people seem to be, so what hell.
I'm a straight female.
As far homosexuality and bisexuality, I have zero problems with it whatsoever and believe it should be included in games as a choice for the player to do themselves, and maybe get hit on or asked about by gay/bi characters (granted, yes you should be able to say "No, I'm not interested." of course.) If people are freaked out by the concept of being hit on, (most notably guys seem to be the most immature about it), too frickin' bad, gay people exist, get over it. You should be flattered that someone finds you attractive not horrified, they aren't going to rape and skull-fuck you because they're gay or bi, just say no and move on.
As far transsexual characters, if they were already transitioned, passed and were living as their desired gender, you likely wouldn't know in the first place and it wouldn't even be mentioned. And if you put a stereotyped trans character where they obviously don't pass or even act appropriately like the gender they're living as, which is how you usually see the trans-people portrayed in the media, it would be straight up completely offensive. Overall, properly representing transsexuality in a video game would be extremely hard to pull off and be quite out of place most of the time.
If you focused on them before transition and some character who obviously didn't fit the particular gender they were assigned at birth, it would be rather strange as to why they're on some mission to save the world (which is what most game storylines boil down to at some point) in the first place, when they've got problems to sort out already. Not to mention if they did decide to ignore the issue and join the hero group anyway, it's unlikely they would bring it up out of nowhere and start unloading those personal problems onto the player anyway considering they're trying to save the world.
The only other scenario I can even think of that might even remotely work would be having a romantic interest who passes that the player can choose to flirt with and so forth. Eventually when things get serious into the physical contact zone, the character could tell you they're transgendered and ask if you're ok with that, which the player could respond to how they like. Although, that would most likely come across as some kind of cheap surprise ending or would likely draw way too many comparisons to The Crying Game. (Note that in this circumstance, the person would pass and you wouldn't know otherwise until they told you, which contrary to popular belief does in fact very much exist in real life. This would most likely also be someone who is post-op as well, so get those weird "dickgirl porn" ideas out of your head people. The chances of actually finding a trans-person who actively enjoys that is rather slim.)
Outside of that... There's also transvestite characters. Seeing as how transvestism is a sexual fetish, I'm not sure what purpose it would really serve and how you would even use it. The whole stereotype about a straight man dressing in gaudy women's clothing and wearing copious amounts of makeup because it turns him on is actually extremely accurate to real life. Although, I don't know how exactly you could make a situation were it would be handled in a "serious" manner unless the player had to go to a crossdressing bar or something, and even then, it just seems gimmicky or some sort of strange joke. Also, the downside is that a large portion of the general public doesn't have the slightest clue that transvestite and transsexual are two extremely different type of people and it would most likely not give any sort of positive effect for the transsexual community in the end, which it already does.
Only scenario I can even think of that is vaguely inspired by transvestism might be having various characters wearing certain types of clothing that is deemed inappropriate by society for their gender, or a male character wearing somewhat feminine makeup or something. These characters could be represented in the sense of just wearing whatever they feel like and potentially allowing the player to question the stereotypes of gender appropriate-dressing. However, that's not really enough to put into the actual transvestism demographic, and would be more simply pushing social boundaries, which could still be interesting, but it's not going to represent transvestites. As it is, a kilt being used in American culture is seen as pushing social gender boundaries, but that doesn't make Scottish men transvestites.
