So I'll address these claims because I see them brought up very frequently, even though they are irrelevant.
'Your genitals determine which gender you are'.
They don't always; when somebody's gender identity does not match their genitals they are usually described as 'transgender' and an extensive body of research exists on transgender people, showing that their predicament has biological causes, such as ambiguous brain structure, perhaps generated by foetal hormonal imbalances:
Causes of transsexuality - Wikipedia
Even if somebody's gender identity always
did conform to their genitals, some people are born with genitals that are neither fully male or female.
Intersex - Wikipedia
Hence the existence of people who have ambiguous gender identities, that do not conform to the prevailing binary, is completely expected.
I personally feel like it reinforces gender stereotypes. Why assign certain aspects of your personality to the expression of one gender or another based on how you feel aligned that day/week/month etc? Doesn't that just foist the actions you are performing onto that particular gender and show you believe they traditionally ought to be doing those things, rather than doing away with gendered performance altogether and treating everyone equally, as most LGBTQ+/other social activists and advocates claim to want? I don't know... Why not just be "you" rather than a label? That said, do what you want as long as it doesn't interfere with being a productive member of society. I really don't care what you think/feel/believe/"know" you are, and it's not my business to.
My two cents.
I think this is the wrong end of the stick, so I'll use an example of a sex-ambiguous behaviour observed in homosexuals to clarify it.
It has been widely observed that children who turn out to be homosexual routinely prefer to play with toys associated with the opposite sex:
Childhood gender nonconformity - Wikipedia
This observation does not mean that homosexuals support gender stereotypes, and obviously gender roles that apply to children- such as 'boys prefer to play with cars and girls with doll houses' are still socially constructed, by virtue of the fact that cars and houses are literally human constructs- cars and doll houses only exist
because we construct them.
What this actually shows is that humans are probably predisposed to produce social constructs of conceptions of gender, and that humans are innately predisposed to take interest in the activities that are designated to their gender role. (the designations are themselves arbitrary- we could imagine a world in which all women wore trousers and all men wore skirts, for example, and then men who wore trousers would be perceived as cross dressers)
Some humans don't fit into this designation, and this can manifest as an innate affiliation with activities and rolls which are normally designated to the opposite gender.