The particular study linked to by NatyoCheese was a paper presented at conference which made big claims based on tiny differences.
The number one issue is that when you look closely at the measured differences what you will typically find is not that the measurements of males who have been diagnosed with and treated for GD are the same as those of females in general. Instead they deviate from the measurements of males in general in the direction of measurements obtained from females.
That's a whole universe away from the claim that the brains of males who identify as trans have been shown to be similar to, let alone the same as those of females.
Furthermore, we're looking at an extremely small number of measurements in an amazingly complex system that could deliver many thousands of measurements. So there's a lot of wishful thinking in play when these claims are made. Understandably so - gender dysphoria can be an incredibly distressing condition with life-limiting consequences for its sufferers. I'd want to know, too, what had caused me to suffer so much.
One of the few things that seems to be supported by neuroscience, is that some measurements of some brain structures/functions and/or responses of homosexuals show similarities to the opposite sex.
But this paper seems to make no mention of sexuality. As pre-adolescent children diagnosed with GD often turn out to be homosexual, only a long-term follow up would allow us to see if the measured differences are anything to do with GD at all. If any such paper doesn't correct for sexuality, I would want to know why.
There's also the problem that our brains are plastic - they change constantly. Our brains respond to whatever life throws at us by changing and adapting in a number of ways. Are we measuring differences because the brains of these individuals are being reshaped by particularly strongly stereotypical pursuits and behaviours associated with the opposite sex?
And drawing conclusions from the brain scans of small children about GD is particularly fraught with problems - they change so rapidly that a rescan just months later may well show a different picture.
One recent interesting result of these studies has been a measured difference in the region of the brain coded for an individual's perception of themselves, including their body image. Those measurements in people diagnosed with GD were remarkably similar to people diagnosed with Body Dismorphic Disorder, suggesting that what underlies these conditions is a change in an individual's self-perception which then manifests in different ways.
However, it has so far been impossible to determine whether this measured difference is the cause or the result of the condition these individuals are diagnosed with.
More importantly, as the current minimum standard for trans inclusion is a verbal statement of identity, brain studies are not all that relevant to our fight. Few males identifying as trans have a diagnosis of GD, in light of which these studies seem quite irrelevant to the overall issue of including males who identify as trans in female-only provisions.
Furthermore, there is no evidence that males who identify as trans pose less risk to females than all other males. There is however evidence that males who identify as trans pose the exact same risk to females as all other males.
To date not one study has ever proven (or even looked at) whether these minute differences could possibly alter male pattern behaviour or male pattern sexuality to the point where these males are sufficiently different from the rest of their sex class that they pose less risk to females than all other males.
Which means that these studies are interesting for those seeking to explore and understand the causes of gender dysphoria. But for those of us seeking to defend women's sex-based rights, they are a distraction at best and a waste of time and energy at worst.