Scientist here; will do a more complete breakdown when I don't have other papers to read but wanted to share some preliminary thoughts. (Also, Kai, I pinged you on Twitter! I wanna be friends!)

You and sneeuweekhoorn nailed that the MTF brain scan is inconclusive and that if there were truth in the matter, brain scans would be used as a diagnostic criterion. And you're right, the conclusions the authors are drawing are far too strong for the data they're presenting. I'll try to keep it short.

1. The question the authors are considering in this review paper is not "do male and female brains exist?", it's "well DUHHHHH male and female brains exist; can we identify what makes brains male or female?" Right off the bat, if a study assumes a certain hypothesis is true, it cannot prove or disprove that hypothesis. That's like if a paper came out that said "okay, we think children's diets influence what kind of TV they like. We found that kids who ate more bacon preferred cartoons, and kids who ate more bread preferred live-action shows," and then the media picked it up and said "look!! They found a correlation, so that must mean their initial assumption was correct!" Makes no damn sense. In order to convincingly argue that prenatal factors determine---or even influence!---an individual's gender identity, one would have to at least cite a study that actually does rule out the null hypothesis (that is, that they do not). To say nothing of correlation and causation.

2. The study is disingenuous in the way it pits pre- and postnatal factors against each other. In this and at least another paper, they repeat this sentence: "there is no evidence that one’s postnatal social environment plays a crucial role in gender identity or sexual orientation." A careless reader might interpret that as "alas, many bigoted scientists have tried for years to claim some environmental connection to gender dysphoria, but they have all failed," when what the author really means to say is "due to lack of evidence, we cannot rule out environmental causes as a factor that influences gender identity." Again, gender is a social construct and social constructs aren't introduced in utero, so the first case makes no damn sense whatsoever.

3. And like---can't something be influenced by both nature and nurture? It's not like they're mutually exclusive. But these authors claim that because they found prenatal factors "that influence gender identity that may result in transsexuality," surely gender identity cannot possibly be affected by any postnatal factors.

4. Omg, that reference they cited for Table 2 links back to a ANOTHER review paper with almost the same name written two years before by the second author. Dying. Gimme a sec.

5. The Programmed gender identity is irreversible section; just the whole thing. Putting aside---with some difficulty---that this section consists of a single case study and ends with citations to two papers from this lab, one of which is the aforementioned earlier review paper and the other of which has jack all to do with gender identity, they sure are throwing around words like "irreversible" and "permanent" despite having no evidence that this is the case for gender identity.

6. This:

In addition, a female INAH3 and BSTc have been found in MtF transsexual persons. The only female-to-male (FtM) transsexual person available to us for study so far had a BSTc and INAH3 with clear male characteristics (Figs 3 and 4).

LMAOOOO. Can't have error bars on a cohort of 1.

7. This is not the original authors' fault, but because I'm guessing this male/female brain theory is being used to justify all sorts of weird stuff, it's worth mentioning that this paper doesn't say anything about how GID should be treated or how the number of CRH-immunoreactive neurons in the PVN makes someone prefer blue over pink, for example. I'm just gonna go out on a limb and guess that people are using this paper to argue in favor of/against things that are not in the paper.

To wrap it up, yes, there are probably some sex differences in the brain and yes, brains are complicated, but there's a HUGE gap between what this paper says and what people want it to say. 'Sex hormones influence brain development prenatally' is such a far cry from socially relevant conclusions this paper didn't draw, such as 'trans people are the gender they say they are' or 'women are idiot dum dums who are bad at math.' But part of this is on the authors for basing part of the review on incredibly strong claims they couldn't substantiate.

Like I said, this is preliminary, but I'm happy to go into more detail if prompted. (Edit: formatting)