My view is that, point two is flawed, point 3 is wrong, and point 4 is dangerous.
What we call gender is the cultural expression of sexual dimorphism, which is very real. Gender therefore is not automatically a system of control. It's a story we tell ourselves about who we are. It's possible to tell different stories, and it's possible to negotiate with the boundaries, but it's insane to imagine it as an artificial construct which is imposed on people. (What genius in the distant mists of prehistory imagined it I wonder).
By describing gender as an artificial system of control which is omnipresent and enforced, you actually perform quite a neat rhetorical trick. You make everyone who does not buy into your ideas complicit in an oppressive system. By so doing, you justify the use of violence against anyone you perceive to be enforcing gender roles. Which, as established, is damn near everyone.
Effectively, the gender theory is rather like some of the mutant versions of Christianity that hold that only faith in Jesus is required for salvation. It's a way of making yourself part of an elite, who is able to do whatever they want, and be morally justified in doing it.
Which is how you get the lovely spectacle of straight white men who enjoy masturbating in panties screaming death threats at lesbian women for expressing the idea that no, they don't want to suck dick thank you publicly. It's justified in their minds because, by acting as though gender is real, lesbians are obviously acting as enforcers for this evil system of control.
Basically, look up Lysenkoism (another attempt to ignore biology deemed incomparable with ideology) and it's consequences, and you will understand what gender theory is and what it will do.