The movie "Barbie" is a disquisition on gender, which is the semantic layer of sexuality, especially, on the mystery of feminine gender.
On the biological level there is the obvious sexual difference in the bodies being variedly adapted to producing and exchanging sperm and egg. There is a biological male and female. However, as beings that have evolved language we produce a difference on the semantic level where we signal our sexuality, by emitting and receiving signifiers, to and from other subjects. That semantic level of sex is called gender.
It appears there could be more variety in gender than in biological sex, constrained to a binary structure by nature. Since the gender signaling is motivated by prospects of sexual success then the structure of gender roughly reproduces the biological binary. Yet gender tends to multiply beyond that because it is the semantic part that we enjoy while sex is a goalpost planted somewhere in reality - beyond the reach of signifiers. Without language we would just produce and act on simple provocations - like animal female in heat calling to all males.
Barbie and her Barbieland presents a version of the world where gender is detached from its sexual moorings and floats freely in the semantic space. So it is gender in its pure state. Ken wants to stay over in Barbie house but is not sure what they would do. Barbie has no vagina and Ken has only an unsightly bulge.
Barbies in Barbieland have unlimited access to power. They can be anything - lawyers, pilots, presidents, construction workers. It is not important how or by whom that power is provided, but it matters that Barbies can easily avail themselves of it. In the center of Barbie life is a home - that specially is in the scope of life of the stereotypical Barbie.
Ken's realm in Barbieland is the beach. Ken and Kens approach the Barbies with admiration and solicitation - trying to get closer to them with vague attempts at intimacy - vague because the sex part has been taken out. Kens are anxious about their purpose in Barbieland.
On a trip to the real world (only so real as a typical city center filled with corporate buildings) Ken and Barbie discover new things. Barbie finds her manufactured gender and Ken - the patriarchy, which he immediately imports into Barbieland. Barbie stays on in the real world a little longer to better inform herself about the mystery of femininity. When she returns to Barbieland she finds it replaced by the patriarchy of "Kendom" where anxious Barbies serve the needs of Kens who have become their pimps.
But Barbie, the stereotypical Barbie traveling the real world, has now found out some new secrets about the patriarchy and its deeper motivations. She will start a revolution to abolish the Kendom with the help of the already institutionalized but sidelined Barbies: the lawyer, president, engineer, etc. Barbies are united in their feminist activism which also aims at getting the Kens to fight among themselves. Peace, and justice presumably, returns to Barbieland and to what relief for the intervening Mattel Board of Directors which is the real world patriarchy! Another intervention comes from the female inventor of Barbie -- an old woman hidden in the bowels of Mattel corporate headquarters. Her insights, shared with the stereotypical Barbie, allow us to hang out the chief question of feminine gender, expressed by the haunting musical theme: "What was I made for?" All the while when Ken has no such question since he is not yet made - he has to make himself.