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You can actually change characters genders with a genderbender tool that you can buy in Heracross shop. Or choose your preferences when making a new game file! I believe, Grovyle asks something like "And what sex do you think I would be?" at the very start of the game

Yes and no. Technically yes because you can genderbend the characters to all be male or all be female, and technically no because the gender bent versions of the characters are canonically just a camera filter and some of the characters are more than happy to repeatedly remind you of this point. Especially at the end of the game when one of the characters canonically being a girl becomes exceptionally relevant information.