The premise of this manga is really interesting. Everyone knows they're in a game and what their roles are. Most people try to fulfill their roles. The fate of the entire world depends on the protagonist character choosing a heroine. If the protagonist doesn't choose a heroine, it's a bad end and the universe reboots, with everyone losing their memory and starting from scratch.
The problem is that the protagonist doesn't want to cooperate and insists that he loves the best friend, who he physically can't do anything romantic with (he can't touch him, he can't say certain things to him, etc. because the game rejects it).
The best friend works his ass off to try to get the protagonist to fall in love with one or more heroines, but nothing seems to work.
The various other characters approach their roles in different ways. The rival character doesn't want to be an asshole, but it's his fate to give the protagonist trouble. The teacher despises the fact that she's not a heroine and drinks to cope. It's apparent that at least some of the heroines are only chasing the protagonist because that's their role, not because they actually love him.
The crossdressing bit just seems like typical manga silliness - as of ch. 37 it doesn't affect the story. The best friend character isn't into it and it doesn't affect the protagonist's feelings, but it gives the heroines a way to tease the best friend.
If you're avoiding it because of the BL tag, give it a shot anyway. Unless you just can't stand the idea of a dude being in love with another dude, I guess. The protagonist doesn't seem to be into anybody except the best friend character, and the best friend character is basically asexual (although the protagonist is starting to give him complex feelings, apparently). It doesn't follow the normal BL tropes.