Also you have to keep in mind that as far as the society at large is concerned everyone already perceives Bridget as a girl to begin with and he has had to correct folks day and night. So him deciding he's a girl wouldn't be something that'd surprise people or make them somehow be weirded out by him. This bad end story is about him tiring of having to correct people all day and night and being like "screw it, I'll just be a girl since you all want me so much to be one!", which is a not-unthinkable way to react to constant pressure since birth to be girllike so you won't be killed by your parents, and then people constantly judging you by your looks. This is why you see him be kinda awkward about saying he's a boy to Goldlewis, he's tired of having to do that, and in the good ending he finds the courage to be true to himself no matter how hard it may be on him, like how Ky admits to being a gear openly, despite looking like a normal human.