This will probably be my most controversial post by far, but it needs to be said.
Gendered socialization is unequivocally real. Boys and girls are treated and socialized differently before they're even born.
Female babies are disappearing en masse, because male babies are more valued.
From an extremely early age, parents respond to their childrens' emotions differently based on gender. Mothers over-estimate the crawling abilities of their infant sons compared to infant daughters.
Mothers speak to their infant daughters more and talk them more about emotions than they do their sons.
By the age of 2, boys already show an avoidance to the color pink and other items traditionally seen as feminine, laying the ground work for early demonstrations of misogyny in childhood.
When children enter pre-school, there is no difference in math abilities between boys and girls. But such gaps begin to appear as children grow older.
The vast majority of girls report feeling unsafe going outside, and at least 2/3 of girls have reported experiencing sexual harassment at school by the time they 16.
Further on in education, women will understimate their scores, while men will overestimate their scores. Women will perform worse on tests when first told that women, on average, perform worse.
Researchers argue that the prevalence of sexual assault against women is so high specifically because of early gendered socialization. The men who commit sexual violence consistently demonstrate specific ideals about gender and perform hostile masculinity.
The patterns reach well into adulthood, influencing occupational choices.
I could literally go on and on and on. There are countless studies and entire fields of academia dedicated to researching this. The fact that children are socialized differently paced on assigned or percieved gender is really not debatable.
I am sympathetic to the fact that transphobes have warped the concept of socialization to insinuate that trans women are destined to be violent or predatory, or that trans men are destined to be submissive and helpless. However, people weaponizing these frameworks does not mean that the phenomenon does not exist.
Furthermore, individual people's nuanced experiences with gendered socialization does not mean that these patterns don't exist on a large scale. Any interaction with society will confer the influence of gender biases, especially upon children to are extremely vulnerable to both subtle and overt social cues.
Again - gendered socialization is real. This is a core aspect of feminist analysis. I am not going to pretend otherwise.