According to this chapter, " Chloe" is the female lead of the novel she read. I can't imagine that the author would leave such an important detail that " Chloe" is actually male so Blair probably didn't finish the novel before she reincarnated/transmigrated. I have two theories on the situation of " Chloe".
First Theory: Due to circumstances in the novel, " Chloe" is male and had to crossdress as female for the majority of the book for reasons unrevealed in the novel. In this timeline of the dream ( ?) Blair had, however, Blair's presence caused an effect which made her stop crossdressing for whatever reason.
Second Theory: The current " Chloe" is not the same Chloe in the novel. Maybe this Chloe is a substitute for the actual Chloe for whatever reason. I believe that Blair said that she was going through a dark part in her life right now so it could be possible that this Chloe was sent to take the place of the actual Chloe so she wouldn't have to suffer.
There could also be a chance that Blair has incomplete memories of the novel and may have forgotten that " Chloe" is actually male.