Yes, gender is derivative of psychological sex (or what is often called gender identity, though that is a confusing label because it's not quite like other kinds of identity).
It is certainly not a social fabrication though. People actually, physically, feel cool while under the shadow of a tree.
> and at worst an unmoored fantasy.
This statement is beyond the pale. You should probably retract it.
> Pronouns refer to sex.
This statement is pure, unadulterated gender ideology.
> Stop coercing my language and do what you want with your body.
Some amount of coercion is required to exist in a society—believing otherwise is right-libertarian nonsense. For example, in any reasonable workplace or school setting you are required to not harass, discriminate or retaliate against people. That is a kind of coercion. Part of that coercion is to use trans people's chosen names and pronouns. This is just. In a sane jurisdiction like California it is the law.
Outside of work or school you can do whatever you like.