A few facts:
1.Yes, there is a male brain and a female brain.
Examples:

-Men have 10% larger brains on average
-Women have a higher % of grey matter
-During emotional memory processing, men have greater activation in the right amygdala, while women have greater activation in the left amygdala
-Women have greater cortical thickness
-Men have a higher serotonin synthesis rate
-Women have higher neuronal density in language-processing regions
-Women have higher orbitalfrontal to amygdala ratio
-During resting states, men show stronger functional connectivity in motor and sensory networks while women show stronger functional connectivity in social and emotional networks
-INAH-3 is 2-3x larger in men than women
-BNST is 50% larger in men

2.No, the fact the brain is a mosaic does not matter. People like to talk about the fact that individually these structures are really just group averages and the brain is a mosaic of male and female structures, but when you look at the brain as a whole it really does cleanly fall into male and female brains. We know this because a stanford study trained an AI on resting-state fMRI scans of roughly 1,500 people, and it maintained over 90% accuracy in predicting sex across multiple independent datasets from different research centers. Now some may think that 10% inaccuracy means something but in reality, it just shows the limits of AI and it could have been pushed further with different methods or given more training data

3.These structures are definitely built by prenatal hormones. Not by x or y chromosomes (with some exceptions). We know this because when looking at structural MRI, fMRI and DTI of people with complete androgen insensitivity syndrome (CAIS), their brains are completely female typical in all the areas you’d expect. CAIS is a condition there the androgen receptor has a loss of function mutation and therefore cannot actually read the testosterone in the body, which makes the fetus develop along a female-typical pathway despite having xy chromosomes. The reason x and y chromosomes are talked about in sex is just because the y chromosome contains the SRY gene which starts the production of testosterone and turns the fetus into a male, that’s literally it. And the absence of that would make the fetus just develop along the female-typical pathway. But whichever pathway it develops on is entirely contingent on actual prenatal hormones and sensitivity to the hormones. Those with CAIS exhibit completely female-typical interests, social behaviour, sexual preferences, and a female identity. No, this stuff is not caused by socialisation, because when looking at those with a 5-alpha reductase deficiency, they’re socialized as female and born looking female but still have male-typical interests, social behaviour, sexual preferences and a male identity. A 5-alpha reductase deficiency is when testosterone fails to convert to DHT, and DHT is required for genital masculinisation but not necessarily neural masculinisation, which is directed by testosterone.

4.No, unless you have a rare genetic disease, prenatal hormones cannot be changed enough to make a sex switch in the brain. There’s a pretty narrow range for variation within sex when it comes to prenatal hormones. Yes, some differences in testosterone or changes in timing of testosterone may change the brain slightly, but overall it’s still fairly sex-typical. The absolute difference in male vs female androgen signalling is massive.

5.No, trans people actually do not sufficiently differ in their brain structure compared to their sex at birth, which is exactly what we would expect given all the other information. Sure, a few papers with a small sample size and ideological driven funding may show small local changes compared to their assigned sex, but these papers are more focused on finding the differences between their assigned sex rather than looking at the big picture, which would be that the vast majority of them, if not all of them, would still have an overall brain that looks typical for their sex assigned at birth