You never know we may see concrete physiological differences and evidence of the existence of trans-people
Perhaps we will.
And if we do, those things will still not mean a trans person's inner feeling of gender is interchangeable with actually being person of the opposite sex, nor justify their appropriating the name and resources of that sex.
Because whether gender exists or not, sex, undeniably, does exist. And wanting to be a different sex is not the same thing as being the opposite sex.
And gender, even if we discover that it also exists as a concrete, physiological thing independent of cultural constructs, is still a different thing to sex.
So, even if gender does exist, there is still no logic whatsoever in the claim that the words we use for sex, Man and Woman, somehow "really" meant an as-yet-undefined-and-undetected different thing all along.
So believe anything you want to believe about yourself. Find kindred spirits and give your thing a whole new name. Form a political movement for rights based on your thing. All fine.
Just don't take the name of something that already exists then demand everyone starts using it for your thing instead.