@DadJoke
The difference is that most gender critical people think that gender identity is a belief. Not a single person has provided any peer-reviewed evidence that this is true. Most scientists use the term to mean an innate sense. They research its causes. They don't question its existence, any more than you would question the existence of sexuality at this stage in history.
If gender critical people acknowledged that people have an innate sense of their gender, which usually aligns with birth sex, we can then discuss how we as a society can deal with that.
This quote is an important one, because it states that we must acknowledge the existence of a concept which is unfalsifiable (not amenable to scientific testing to find if it exists in all people or not) before we can even discuss this very question, i.e., if gender identity, defined in this exact way actually exists.
Science, based on our current arsenal of scientific concepts, can't address unfalsifiable concepts such as whether angels or demons exist, whether transubstantiation is real etc.
The concept DadJoke describes here is a belief which the gender identity ideology is forcing on all of us, the way religious beliefs are forced on people in theocracies.
You have to read carefully to see that a very particular definition of 'gender identity' is used here:
It is supposed to be 'innate', implied to exist in everyone, and only happening to 'align' with biological sex of the person, rather than being based on it.
When someone is asked why that person accepts the label 'woman' or 'man', it's not at all clear that the answer wouldn't be based on what the sex of that person is. Indeed, I would argue that for most of us it IS based on our sex, on what others told us about the name of people of our sex, and on how the society treats us, on the basis of that sex.
So when someone says that everyone has a gender identity that person might mix together definitions which indeed equal that innate-not-based-on-sex one with definitions which just mean that people know what sex they are or that they know what their society calls people of their sex.
TLDR: Science can't address the question of whether unfalsifiable concepts exist or not. That's why we mostly try to keep religion and science separate from each other.