Immune Cells Play Key Role in Determining Male or Female Traits in the Brain

The paper explains,

According to this maternal immune hypothesis, cells (or cell fragments) from male fetuses enter the maternal circulation during childbirth or perhaps earlier in pregnancy. These cells include substances that occur only on the surfaces of male cells, primarily male brain cells. The mother’s immune system recognizes these male-specific molecules as foreign and produces antibodies to them. When the mother later becomes pregnant with another male fetus, her antibodies cross the placental barrier and enter the fetal brain. Once in the brain, these antibodies bind to male-specific molecules on the surface of neurons. This prevents these neurons from‘‘wiring-up’’in the male-typical pattern, so that the individual will later be attracted to men rather than women.

It doesn't, but apart from this study the mothers's body is somehow able to remember how many sons she has had and influence the sexuality of her later sons. This memory of past exposure to a foreign object (i.e. a foetus) is the hallmark of immunology.

I assume that it would be the mother’s immune system (sensitized by previous pregnancies) response affecting the fetus while in utero.

Gender dysphoria also isn't a clean distinction between "male" and "wanting to be female". The underlying phenomenon is observed to be rooted in sex-specific instincts and feelings inverse to what is normally found in people of the same sex. The interpretation is cultural. Indians believe it means there are two spirits in a single body, Mexicans have the "mux", and even in the west there's been tacit admission by some trans people that they feel different but couldn't tell you they were actually female...the oft-maligned "nonbinary".

So really, I don't personally believe a brain can be cleanly male or cleanly female. Rather, if specific parts are formed differently than usual, then they respond differently to external stimuli. This can result in a wide range of sex-atypical behaviour ranging from mere homosexuality to finding one's genitals revolting. How you interpret that objective phenomenon is really up to the individual.

To grossly summarize a cocktail factoid - bird cells can individually differentiate, and some birds are truly half and half. Us mammals bombard our cells with hormones, constantly telling them how to differentiate, as though we were some sort of eusocial insect colony.