Gender on it's own is difficult to pin down because more than anything it's a way of feeling, of knowing what you are.
Feminism has long fought to break down traditional gender roles, to untie the notion of, for example, caregiving or providing from the genders they have long been associated with. The understanding is there, that the things you do should not be and are not dependent on the gender you are. None of that changes by opening up the space for people to say they are a different gender to what they were originally classified as.
There's a tendency to ask trans and non-binary people to be able to explicitly prove something about their gender, about how they feel, about what gender is at its very core, before they can be allowed to be that gender. That's something not expected of cis men and women. And it's a nifty trap because of how almost impossible it is to do.