Not... Really? That's a very culture and expression forward veiw of gender which as more questions get asked widely is seen as a very cis centric veiw of gender.
Like we haven't really nailed everything down and a lot of Non-Binary people don't like this take because a lot of them find it invalidating but the trans and cis aspect of gender are very different. The more we inquest into how the average cis person experiences gender the more we find the majority of cis people are all kind of "Non-Binary" they don't feel implicitly like their role holds any super deep meaning and feel like if their body flipped to the opposite sex then that isn't horrifying. The idea that cis people have a built in gender compass that aligns with a single set of sex characteristics is taking a trans lens and assuming that's how it works for everyone whereas if a big room full of cis people actually talk to each other about whether they have any kind of innate feeling of being male or female aligned you start realizing that premise of actually having any massive non-cultural preference one way or the other just isn't the norm. Cis people just don't have to interrogate their gender the way trans people do.
Basically it's like the brain's most common configuration is it's wired to accept whatever outcome of puberty and be flexible enough to adapt.
The trans aspect of gender (and a minority of cis people) is entirely different. We react to our sex characteristics intrinsically outside our control not as having neutral value but as having either negative or positive value. We are internally reinforced to react either with rewards like joy when our bodies are reflected back to us as matching our pre-settings oe punishes with stress, jealousy and depression when sex doesn't align. Like a body expectation switch got stuck in one position and anything other is abhorrent.
For trans folk gender expression and cultural reinforcement is just a mirror that causes other people to reflect our bodies back at us. Gender expression becomes a tool like technology to communicate needs. Indeed a lot of trans people have issues with having to overperform gender not because they want to participate in the culture but because we are steering people to avoid seeing our bodies, scanning and verbally reporting back to us their physical assessment of our sex... that hurts us and so we have to perform the most readable cultural expressions of gender to get strangers to understand at a glance how to help avoid our poisons and to treat us in ways that hit the built-in reward trigger.