I'm willing to believe that masculinity is on a spectrum
So am I. I'm actually quite sympathetic to the "lady brain" thing. I could be sympathetic to the concept. If it was a useful model for reality.
But not only is monitoring for lady brain impractical versus the long-established alternative of checking for the "lady body", it's blindingly obvious that the vast majority of current transwomen have extreme "man brain". Every direct observation and every aggregate statistic shows how they're further away from women on the "masculinity spectrum" than the average man.
So "lady brain" as a hypothesis for transgenderism makes far less sense than "cluster B personality disorder brain".
Meanwhile, over in trans land, it's all just a text-based role play. They're not actually attempting to model the real world, they're just manipulating text. "A trans woman is like a woman because she's a woman, and obviously a trans woman must be able to use women's spaces. And anyone who's objecting must be transphobic, because the only difference between a trans woman and a woman is the 'trans'."
They're just all doing the role play of supporting the civil rights of this imaginary "trans woman", in a way that would make sense if "trans women" were actually a real type of woman. Which in the real world, or indeed any sort of logical framework, they're obviously not.