Gender performance is the theory is that people are expected to behave in certain ways in order to demonstrate that they are good/correct/successful members of whatever gender. That is, gender is a set of behaviors that people are demanded to perform.
This is seen clearly in childhood, when if a boy is seen to be unmasculine, or a girl to be unfeminine, they are ridiculed by their peers and often worried-about by their parents or teachers. It is no accident, I think, that the meme of "cooties" is closely associated with the age group at which boys and girls begin to differentiate; it is an Ignoble Lie that serves to enforce the gender binary, to dig a trench between the two emerging camps.
The concepts of cooties, and effeminacy, and mannish women, and so many other things, are tied very closely together. The common undercurrent here is: stay well away from the things associated with the1 other gender – or you might get some on you. A person who fails to perform their gender, who begins to pick up associations with the other gender, is treated as contaminated, and thus inherently suspect.
Adults, and especially liberals, like to believe that we've outgrown this. However, there is a parallel phenomenon, a pattern of behavior that follows the same shape and pattern, that's quite widespread in the adult world, even among people who are much more relaxed about gender.
Rather than a war of the sexes, these battle lines are drawn around ideological factions, and especially political parties.
For example, politicians like to accuse each other of "socialism" – not bothering to claim that there's anything specific actually wrong with whatever policy proposal, but rather simply claiming that it's contaminated with socialist cooties. It resembles socialism, and therefore eww gross you got some on you.
This sort of thing happens all the time, from every direction. Gun rights activism is associated with masculinity, both by proponents and opponents; social aid programs are smeared as handouts; military spending is portrayed as belligerent, bullying, and imperialist.
The effect of this is that people trying to engage in policy debates are forced to defend, not the substance of their proposals, but the aesthetic character. We do not ask whether something is a good or bad idea, so much as whether it is a left or right idea. It becomes inconceivable that the other side might have any good ideas, because if you ever go anywhere near them, you might get some on you.
Once your reputation has been tainted, contaminated with cooties from the wrong party, your proposals are treated as inherently suspect.
This system is vile and horrible and I want to burn it to the fucking ground. In all its incarnations, gender and political and otherwise.
1. Nonbinary people exist, but the mode of thought being discussed here tends not to acknowledge them.