I think it's straight up offensive to tell someone they can't or shouldn't play a game because of their gender. If a guy likes otome games, he should be allowed to play them. If a girl likes, I dunno, racings games or first person shooters, she should be allowed to play them. Games exist for enjoyment. If you like it, why shouldn't you be allowed to play it?
Otome games, by definition, are female protagonists with male love interests. It doesn't make sense for someone to demand that BL be included in these games. Same as I wouldn't include female love interests in a BL game. However, if a creator WANTS to make a game where you can pick your protags gender, or a game that includes both male and female LIs... there's nothing wrong with that, either.
I don't see the point in demanding an otome game have BL, or a BL game add female LIs because they are two different genres meant to cater to two different tastes. Nothing wrong with either of them. I also don't see the point in getting mad about a creator wanting to make a game that allows more freedom regarding your protagonist's gender, or different options regarding your LIs - so long as it's clearly labeled on the tin. If I know what you're selling, then it's way more likely that I'm going to be happy with what I'm buying. There's clearly a market for all three kinds of games.
Last... I don't think there's anything wrong with someone who likes a game that is BL or otome creating fanfiction or fanworks that don't align with the original vision of the game. Fanfiction is an escape from cannon. Take any movie or tv show or game, and you're likely going to find someone creating both straight and LGBTQ+ fan content for it. What's the problem? It's something they enjoy, they're not hurting anyone with it, and they're not forcing you to consume it. Just because I don't like reading about, I dunno, Loki/Darcy doesn't mean that I'm going to be mad at other people for drawing/writing/enjoying it. Or just because I think Tony/Loki is adorable doesn't mean I'm going to shove it down everyone's throat.
As long as fans respect each other, there's no reason we can't all have different tastes.