Gender identity is important because a whole lot of people have one, and to them it describes some part of who they are. This isn’t just about trans people, either; there are a far greater number of cis people who have a gender identity than there are trans people.
For better or for worse, the gender that a person expresses largely colors how the world interacts with them. Most people who have a gender identity feel that something about the nature of this interaction feels correct or natural, and are comfortable using that context as a basis to conceptualize themselves and to structure their interactions with the world.
This mostly happens seamlessly, until we get to trans people, who have the wrong identity chosen for them, and are effectively forced into an interaction with the world that feels very much incorrect or unnatural. Fortunately, we now have tools that can go a long way toward fixing this problem, though trans people face a lot of resistance to accessing them.
It’s important to note that identity means “I am,” not “I should be” or “I want to be.” An identity is a core idea that a person holds true about themselves, one which they use to define who they are. It is not a whim or a notion, and for the most part it cannot be changed.
I’m of the belief that there are a number of people out there with weak or no gender identities. I see nothing wrong with that, but it’s important for those people to realize that their understanding of gender is not the same as other people’s. They haven’t transcended the idea of gender by thinking the right way, or by actually making an effort to avoid sexism. They simply don’t have a strong gender identity, whereas other people do. Neither of these is inherently better, and there is no cause to be proud of or to blame others for either; gender identity is an identity.
For those of us who do have a gender identity, having one does not in any way imply that we support gender stereotypes or even the binary system of gender that leads to people having gender identities. It doesn’t mean we’re inherently sexist, or that we think being a man or woman means any particular thing about a person’s competencies what roles are suitable for them.
But it does affect our lives, and to us, it is very much important.
The only time anyone ever really talks about gender identity is regarding trans people, and as a result, the only time anyone ever criticizes gender identity is also regarding trans people. Cis people always seem to get a free pass, even if they have strongly held gender identities! And given how cis people are the ones who collectively have the power to actually do anything about this, any criticism of gender identity when talking about trans people is inherently cissexist.