Specifically COG games? I don’t think there are any but I could be wrong. However, I’m specifically talking about a few that I know are Hosted ones. The Infinity series and the previous installments of the Foundation of Nightmares (Sorry, forgot what they’re called) are gender AND orientation locked. (This is not a roast or insult to the authors. While I do not want to read those stories because of it, I feel its their right to bring the stories they want and I’m sure they are written very well.) There are plenty of other games that are male only and ofc Great Tournament is orientation locked. I usually delete and don’t bother with games that don’t let me play the way I want to, so I’m sorry I can’t give you a comprehensive list.
I’d also to like to say that there are quite a few who end up effectively locked because only straight male characters (and sometimes lesbian characters) actually have options that work in happy endings or are easily accessable. I don’t want to give spoilers for said games though but I’d be happy to elaborate if needed. (EDIT: I’m aware this might come off as moving the goal post, but it was part of my original intent behind my original comment. Because I’m LGBT+ I’m very much aware of how the media portrays LGBT+ relationships especially in the US. AKA either its inappropriate to have said characters or relationships even if it’s G rated or they have to be villains or die horribly as a moral story.)
Basically, while I agree with you that I would much rather have games with more choice when it came to forming my characters, I wanted to defend this person’s vision specifically because I only really see the level of push back on this something that is specifically catering to lesbian relationships and not the others that go in the opposite direction.