Not necessarily. Innate gender identity could be to do with how we experience our bodies, or some kind of sense of selfhood which isn't yet understood, but which has nothing to do with aptitudes, personality or behaviour. From a scientific point of view we don't know what gender identity is or how it functions. What we do know is that something which appears to look like transsexuality, or discordant gender identity is widely observed in many different cultures, that millions of trans people exist and pay a significant social penalty for being trans and that studies on intersex children attempting to negate gender identity have been at times tragic failures. That suggests there is something going on, something which is no doubt magnified significantly by patriarchy, and which we don't yet understand very well, which isn't unusual because we don;t actually understand brains that well.
But on a more pragmatic note, gendered society is real and 99.99% of the human population plays along. Even if gender dysphoria is merely an intense discomfort and dislike of the gender role you have been assigned, or a significant attraction to being of the opposite gender role then isn't that something that can, and perhaps should be accommodated? Cis people flaunt their gender all the time, our entire mainstream culture is largely based on it, and even if we oppose that it only seems to be trans people who are attacked so relentlessly for expressing gender.