I don't disagree with any of this.
From the post that you don't disagree with :
“It would be unreasonable to conclude that gender typing is strong and stable throughout life”
That statement contradicts everything you have said about trans children.
In support of your argument that these children are born trans and fixed for life, you've been selectively quoting the work of a person who has explicitly contradicted that point of view.
Because the child's identifies themselves as being in the "wrong" category you are all assuming this "mismatch" must / can only logically have come from learning about gender stereotypes , and subtle parenting cues . But that doesn't follow and actually there's no good evidence to support that theory.
That does follow and by denying it you show your lack of understanding of child psychology. There is good evidence to support that theory.
I did just one Google of "is there research into how parents influence their very young children with micro gestures"
and the response that I got is summarised below. The actual query follows with pointers to research papers that I suggest you follow and read.
Yes, there is extensive developmental and neurological research into how parents influence very young children through subtle nonverbal cues, often referred to in developmental psychology as micro-connections, micro-movements, or dyadic attunement.
Rather than viewing parenting solely through major milestones or grand lessons, researchers use microanalytic coding (analyzing video interactions frame-by-frame) to study how split-second movements shape an infant's brain, language development, and emotional security.
This is how care givers, wittingly or unwittingly, mould children into what they, consciously or subconsciously, want them to be.