i'm curious as to why you seem to think earth c is "where the only difference between male and female is at most pronouns." i don't see ANY viable foundation for this in canon... though there's not proof to the contrary, it is still a society built to mimic earthern pop culture. it's also significant to consider that june grew up in a world with gender as a solidified concept. i also think even within a post-gender world there would be people who would want to change things about their presentation regardless of their identity or in synchronicity with it; though i can't personally see beyond sociocultural bounds and i doubt anyone truly can i'm still confident i would, at the very least, have landed on shorter hair and a different name in a world without gender.
on a more personal level i do resonate very strongly with june as someone who is, in comparison to their peers, transitioning pretty fucking late. transition doesn't inherently entirely alter who you are as a person (though it can, especially if a good deal of your interaction is defined with dysphoria and depression). i definitely understand being hesitant about june in fear of losing key aspects of her character (hell, ive seen plenty of it in fandom), but i'd hope that the hsbc team doesn't go that route.