What these people refer to as "gender ideology" is actually just slightly more advanced science. Gender is a real thing that exists in the brain, multiple means by which the brain and body can develop contradictory gender/sex characteristics have been identified, and almost 150 years of scientific research support the validity of transgender people and the benefit of gender transition for people who need it.
Its similar to the "there are only two genders, that's basic science!" Yeah, you're right, in the way that in basic science there are only 3 phases of materials. Then you get to more advanced science and things change.
What do you mean gender exists in the brain? It's my understanding there is small but insignificant differences between cis men and cis women brains, so why would a trans person have a brain that "proves" they are more like a man or woman? What does a non-binary brain look like? A lot of early science tried to paint women as having inferior brains than men, women are more emotional while men are more rational because men have slightly bigger, heavier brains. The research is at best inconclusive.
I can understand trans people might feel some euphoria about it but I don't buy the whole boy/girl brain thing. Trans people are valid and can benefit from transition however they choose to do so. I guess maybe I am a radical because I think gender as a social construct (like all the roles men and women have) is dumb and should be abolished.
I tried looking up more about this and this wiki mentions hormone differences, everything else looks very much debated.
The difference between make and female brains is very VERY small, but it's not immeasurable. The critical point is that the differences seem to be exclusively concerning 1) the brain's "map" of the busy, ie the brain is wired for certain hardware, and 2) reproductive instinct.
But even those areas are not 100% predictable, ie everything is a spectrum.
Estrogen signaling pathways identified which tell the brain to develop as one gender or the other, as well as mechanisms by which physical development can happen in one way while brain development can happen in the other https://www.nature.com/articles/s41598-019-53500-y
They mean that gender is a made up human construct and not something that's naturally binary. Gender is a spectrum and the idea that binary genders is the only option is limiting and just flat out wrong.
We can talk about sex vs gender and what means what but at the end of the day gender is more just how people identify themselves.
I vote, if the law gets passed, that every self-respecting individual calls the people who would support such a law as transgender just to piss them off.