Personally, I would not care at the slightest, kids are kids. They could have various inclinations, like boy could be intresting in something more related to social things and prefer dolls or girl can really like cars and mechanics. It doesn't matter, just as your education and hobbies do not change your sex.
The promblem rises up when various degenerates come up with a term "trans kids". If anything on the Iternet makes me mad, this is it. Kids can't be trans, they are kids, if you believe they can - you are a groomer. In general IDGAF about adults being clowns and mutilating themsevles for the sake of trooning out, it's their business and more lulz for me, but leave the kids out of this brainrot. When you see "a trans kid" it basically translates into "their parents are mental fuckers". The gov can deprive you from parental rights for beating your kids (the right thing) but can't if you groom them into chopping off their organs, this is some deeply unfair bullshit.
The thing is that the trans kids narrative follows naturally from the claims troons are already making. How many times have we seen an MTF bitch and moan about not having had "the childhood" movies and anime promised them? All of this is evolving out of a fetishization projecting itself backwards onto the trans people's childhood. They lack the self-awareness to separate their idealized fantasy from reality. They're hardly the only group of people like this, but because of the way privilege theory operates, their position at the bottom (or top, depending on how you think about it) of the hierarchy means that no one feels they can "invalidate" their experiences. They are, in essence, using gender non-conforming kids as props in their fantasy, to justify their belief that they were always born this way. In reality, gender non-conformity in childhood is a predictor of being gay, not being trans. Please note that when I say this, I am not claiming that all gender-nonconforming children while grow up to be gay. Much like the idea of gender conforming behavior in children, all we can talk about here are tendencies, not absolute. There is no guarantee that a child exhibiting gender nonconformity will experience or act on homosexual attraction. That's the problem with trying to reify behavioral tendencies into these solid and mutually exclusive identities.
On the topic of gender toy preference, there is a significant amount of
research into human infants that shows a large effect, but note that the most pronounced effects are for very specific kinds of toys (vehicles and motion for boys, dolls for girls), and other toys we code for gender show a reduced effect. Again, we are talking about tendencies, so not all boys and girls will exhibit this behavior, but the sex of a child is a strong predictor of the type of toys they will prefer. (Though I think an interesting point in the meta analysis above is the most pronounced differences occur in forced choice scenarios, where the child must choose one toy to the exclusion of the other. So more evidence for the "just let them play with whatever they want" camp).
You don't even need to go back to "lizard-brains" to explain evolutionarily why that would be the case. It's not like humans escaped selective pressure right at the start of our species, we haven't even really escaped it now. Behaviors and traits that maximize child survival were selected for, including things like being able to carry a baby around while you still work with the other hand (see carry-angle and possibly a reason for preferring dolls). Women's bodies are built around pregnancy and infant care, because it is by far the most calorically expensive biological process humans do (and an absolute necessity for natural selection to even occur!). The woman invests an enormous amount of energy, and takes on significant risks, to produce offspring. This is a biological reality, even if not every woman has children. Troons can pretend that being sluts and pre-teen girls is really what womanhood is about, but ultimately their bodies were simply not evolved under the same selective evolutionary pressures, neurologically and physically they can't escape it.