Well put, @LordOfLA, and I personally agree with you completely. By nature, we categorise what we see before us, most likely stemming from the basic need to survive (and procreate). No offence intended by that categorisation, as you said, it is later, conscious actions (or lack thereof) that may indeed cause such, when our bias and opinions weigh in.
Times and society change and we must learn to change with them or be left behind, but change does not always come easy. 
Well the MC of Undertale is gender neutral so I’d say it can be very appealing. Then again it’s a game in which your gender doesn’t really matter.
That and playing a robit would be awesome.
Yes but traditional English grammar reinforces binary notions of gender, hence the need for genderqueer and a gender people to choose new pronouns. Personally I recognise my cis-person privilege here and I’m more than accepting of people who need to use non-binary pronouns… Even if that offends traditional ideas about grammar 
Writing is what lends itself to having names, genders and other identifying characteristics. It makes things easier (at least in English, and the languages I’ve studied so far.) Easier, however, does not necessarily mean better.
A game where you can’t select traits to model a character (whether after yourself or to create someone new), where they’re completely meaningless, would be unconventional and unusual.
Someone really should make it. For reference, this is the closest thing I’ve seen to it:
https://forum.choiceofgames.com/t/i-am-everyone-storyfire-thread/11785
There are games where you play as an invisible MC. Meaning, in case of a VN, the MC has no character sprite and you are either addressed by name or with ‘you’ or the game plays in first-person perspective. In a few scenario’s this is combined with ‘unreliable narrator’ and leads to ‘the big reveal’ where the MC isn’t human or you were the killer all along. In some cases the ‘big reveal’ actually spoils it for me.
Anyway I think a story can still be compelling without focus on gender/sexuality of the MC. Most games tend to handle romance as a sidequest anyway so it shouldn’t make much of a difference when you cut that part out and play as a gender-neutral/genderless character.
A few games that have FPP with an undefined MC (until the ending that is) would be:
The Moon Sliver
Master Reboot/ Soul Axiom (SA actually has multiple MC’s but you don’t know who you play as)
Starship Damrey
Creatures Such as We offered the option to pick gender but for me it was completely unnecessary. It would have been fine without it for the game itself was more about esthetics than definitions and facts (at least it was for me).
Gender helps intensely with immersion whether you are playing as yourself, or a character you’re making up. I would not mind ENTIRELY if I couldn’t choose my gender, but it’d definitely be annoying converting sentences in my head to match gender I’d like.
As for sexuality-- I love it. Even though Choice Of Games commonly looks over romance, and don’t bother much with it, I plum need it. Honestly, every choice game I’ve purchased so far has been for romance! Though… I’d like to choose what gender my character is attracted to. I think its a major turn off for most people if they’re stuck getting romantic with a character who has a gender they’re not attracted to in the slightest. I’d understand if the book wasn’t meant to be an immersive sorta series where you inserted yourself in, but none of the stuff here is like that LOL
Diabolical handled that quite well, at absolutelly no point in the game did it ask you about your geneder or how you looked, because you already had a mental image of your character before anyway, so the only thing it asks about is your name.
but that game also does something that I HATE about some choice games, that is having you choose if you are interested in men or women in the start of the game and then have all the romanceable characters change gender to match your preference, it feels like everytime I run into a woman in a game like that the game is saying “hey, did you know you could date her?”
I think that the answer to the OP’s question is a qualified “yes”. A story can be compelling without ever mentioning anything about the protagonist but immersion can suffer. I think a good style to write in would be a first person narrative if you want to go this route. In this case it is taken for granted that you are looking out of the eyes of the MC so you can project yourself into the role. Maybe something like Total Recall: the Game? One where we, the player, is allowed to live a fantasy in virtual reality but events cause our perception of reality and fantasy to blur. Austrian accent optional.
If the story is well written I don’t mind not a gender or having to choose sexuilty .
Austrian accent mandatory, one of the best things about the Governator was that distinctive accent.
With CoG or other “choose an adventure” types of games, as long as the author writes well, I am o.k. without sexuality/gender. If the author fails in writing properly, then it bothers me, especially if I feel the MC is male.
With graphical orientated games, if I can’t make myself female, then usually, I can not play the game. Games like Bioware’s Dragon Age series I am able to enjoy but the Witcher series I am not. Witcher books are ok because I am reading about a guy … see the difference?
It often works the same for me, except for the reversal of my preference for the mc’s gender, but note that if I really truly like a game I will make an exception, the most recent being the currently in development “Seven Kingdoms” game.
True, in graphical AA games especially those with an over the shoulder cam,if I’ve got to stare at a bunch of pixels shaped into some character’s back and ass for 50, 100 or even 200 hours, I’d greatly prefer it if said character takes the shape and role of a cute guy.
I agree but I was accounting for the poor, benighted souls who have only seen the, in my opinion, massively inferior remake rather than the entertaining original with Arnold as the lead and Sharon Stone as one of the female love interests.
Personally I loved Arnold’s Conan the Barbarian accent the best.
I don’t think you necessarily have to be able to create your character and specify their gender, although it is fun. It really depends on the game content. If it’s more of a puzzler, it would probably be alright if the game focused more on game events than the inward character. If you’ve ever played interactive fiction like in the Frotz app, you’ll notice that most of the games dont have any character customization at all and this does not detract from the experience at all. However, if you want to make a story more centered around relationships, having the ability to choose gender might be better.