"Why is it that we demand evidence from trans people, and what does it even mean when that evidence is presented in the first place?"

Because without establishing an objective basis for a subjective experience, there is no guarantee that the subjective experience isn't simply a delusion.

This doesn't change the therapeutic approach, obviously. If being trans were proven to be a delusion, the correct approach would still be to support transitioning and to leave us alone to live as we need to live. But what would change, is the idea that the rest of society should be required by law to treat us as women -- to embrace the meme that "trans women are women," to allow trans women in women's private spaces, etc. That's what changes.

"Science in the wrong hands and used for the wrong causes is just as deadly as pseudo-science."

This isn't a problem with science, per se; it's a problem with human beings. Science is a tool; and there will always be some who use it in the pursuit of truth and others who use it in the pursuit of a private agenda. In addition to these, there is also the problem of implicit bias that goes unrecognized by the scientist herself; but this is always the case in the pursuit of truth. Pursuing truth is inevitably a matter of re-examining our assumptions, learning more about ourselves and the world around us. That will never change. It doesn't mean we discard the scientific approach when we don't like the results.

"All of this is doubly so when trans children are discussed. Any study or report is immediately weaponised both sides of the conversation..."

This is true, and tragic. I don't know how we solve this.

"Evidence is never enough to win an argument"

When I was growing up, there was a saying: "A man convinced against his will, is of the same opinion still." Nobody changes their mind about something unless they want to; and that's why nobody ever "wins" an argument. "Winning" an argument means the other side conceded; and nobody concedes unless they want to.

The solution to the conflicts resulting from trans people living in a cis-normative society will always be acceptance by the cis population because they no longer see a reason to treat us as outcasts anymore. This is how gay people were normalized in American society; laws that don't have the support of a critical mass of the population solve nothing, and actually make things worse in the long term. The approach taken heretofore by a substantial bloc of trans activists, of confrontation and contentiousness, has always foreshadowed this result. There is no quick solution to our problem. Time is the answer.

This is not to say that a Gandhian approach would be counterproductive -- not at all. Non-violent, non-cooperation is simply one side refusing to play. It is non-aggressive, simple assertion of our inherent right to self-determination and our equal dignity among other human beings. But that's not a popular view in America.

"if we want normative trans legislation that ensures that trans folks can thrive and lead their best lives we need to set aside the junk science, the wretched media discourse, and create a new narrative based on both rigorous scientific analysis and reframing the societal narrative surrounding non-cisgender identities."

The fundamental problem is the one I mentioned in the first paragraph; and that can't be solved without science, at least in the short term. In the long term, familiarity will lead to acceptance, and we will be given our rightful space by our cis neighbors. And it won't take laws to do it -- not for the most part.

This is how all our social injustices are really solved. Without the heartfelt sympathy by a critical mass of the public, not even wars can be won; and laws don't have a chance.

EDIT: I feel a need to add that this is an exceptionally intelligent article. I have an unusual degree of respect for the writer's insight and boldness.