Of course they are real people. And, of course, they shouldn't be harassed or demonised. It's the way they are being used in the confected 'culture wars' to distract us from the very real and increasing inequality generated by neoliberalism that is the problem.
it just so happens that trans people's brains tend to match the gender they aspire to.
The article you link to would seem to contradict this:
"In other words, there is no such thing as “the male brain” or “the female brain.”
It seems that when trans people and their allies insist that transwomen are women and transmen are men they are accepting the gender binary and/or sexual dimorphism. It's just that they believe their bodies are out of alignment with their 'felt' gender/sex. They believe they have been born into the 'wrong body'.
I am not sure that it is possible to be born into the wrong body. Perhaps it would be better to try to align the mind with the body rather than attempt to do the opposite.
That's if you accept the mind/body duality, which I don't really.
The bathroom talk is ridiculous
I am a man. I don't feel threatened by transmen. But, I don't think the concerns of some women about physically intact males who identify as women being in 'female' spaces should simply be dismissed as transphobic.
Then, there are concerns about young people being 'diagnosed' as trans too young and being prescribed puberty blockers, hormone therapy and even life-changing surgery.
Some of these concerns may be exaggerated, not least by those who have an anti-trans agenda. But, there are also those who are acting in good faith out of genuine concern. They should not be silenced.